NCERT Solutions Class 7 Maths Chapter 10 Algebraic Expressions

NCERT Solutions for Class 7 Maths Chapter 10: Algebraic Expressions is a valuable resource for students. It helps them master algebraic concepts, develop problem-solving skills, and build a strong foundation for future mathematical studies.

NCERT Solutions for Class 7 Maths Algebraic expressions are incredibly helpful for students in building a strong foundation, mastering algebraic operations, and enhancing problem-solving skills. NCERT Solutions offers a wide range of practice problems with varying difficulty levels, allowing students to apply their understanding and develop problem-solving skills.

1.0Download Class 7 Maths Chapter 10 NCERT Solutions PDF Online

2.0Key Concepts in Class 7 Maths Chapter 10: Algebraic Expressions

1. What is an Algebraic Expression?

A combination of variables (letters representing unknown quantities), constants (fixed numbers), and mathematical operations (addition, subtraction, multiplication, division).

Examples:

• 3x + 5
• 2a - b
• 4x²y

2. Terms of an Algebraic Expression:

Parts of an expression are separated by '+' or '-' signs.

Example: In 3x + 5y - 2, the terms are 3x, 5y, and -2.

3. Coefficients:

The numerical factor of a term.

Example: In 5x², the coefficient of x² is 5.

4. Variables:

Letters that represent unknown quantities.

Example: x, y, a, b in the above expressions.

5. Constants:

Numbers that have a fixed value.

Example: 3, 5, -2 in the above expressions.

6. Like and Unlike Terms:

Like Terms: Terms have the same variables and the same exponents.

Example: 3x and 7x, 2y² and -5y²

Unlike Terms: Terms have different variables or different exponents.

Example: 3x and 5y, 2x² and 3x

7. Addition and Subtraction of Algebraic Expressions:

Rule: Only like terms can be added or subtracted.

Example:

3x + 5x = 8x

7y² - 2y² = 5y²

8. Multiplication of Algebraic Expressions:

Use the distributive law: a(b + c) = ab + ac

Multiply monomials, binomials, and polynomials using appropriate rules.

9. Division of Algebraic Expressions:

Divide monomials by monomials using the laws of exponents.

Algebraic Identities:

• Formulas that hold true for all values of the variables involved.
• Some common identities:
• • (a + b)² = a² + 2ab + b²
  • (a - b)² = a² - 2ab + b²
  • (a + b)(a - b) = a² - b²

3.0NCERT Questions with Solutions for Class 7 Maths Chapter 10 - Detailed Solutions

Exercise: 10.1

• Get the algebraic expressions in the following cases using variables, constants and arithmetic operations. (i) Subtraction of z from y. (ii) One-half of the sum of numbers $x$ and $y$. (iii) The number z multiplied by itself. (iv) One-fourth of the product of numbers p and q. (v) Numbers $x$ and $y$ both squared and added. (vi) Number 5 added to three times the product of numbers $m$ and $n$ (vii) Product of numbers $y$ and $z$ subtracted from 10. (viii)Sum of numbers a and $b$ subtracted from their product. Sol. (i) $y-z$ (ii) $\frac{x+y}{2}$ (iii) ${\mathrm{z}}^2$ (iv) $\frac{\mathrm{pq}}{4}$ (v) $x^2+y^2$ (vi) $3mn+5$ (vii) $10-yz$ (viii) $ab-(a+b)$
• (i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams. (a) $x-3$ (b) $1+x+x^2$ (c) $y-y^3$ (d) $5x{y}^2+7x^{2}y$ (e) $-ab+2b^2-3a^2$ (ii) Identify terms and factors in the expressions given below : (a) $-4x+5$ (b) $-4x+5y$ (c) $5y+3y^2$ (d) $xy+2x^2{y}^2$ (e) $pq+q$ (f) $1.2\mathrm{ab}-2.4\mathrm{b}+3.6\mathrm{a}$ (g) $\frac{3}{4}x+\frac{1}{4}$ (h) $0.1{\mathrm{p}}^2+0.2{\mathrm{q}}^2$ Sol.(i) (a) $\mathrm{x}-3$ Expression Terms

• Factors (b) $1+\mathrm{x}+{\mathrm{x}}^2$ Expression Terms

• (c) $y-y^3$ Expression Terms Factors
  
  (d) $5x{y}^2+7x^{2}y$ Expression Terms Factors
  
  (e) $-ab+2b^2-3a^2$ Expression Terms Factors
  
  (ii) (a) $-4x+5$ Terms: $-4\mathrm{x},5$ Factors: $-4,x;5$ (b) $-4x+5y$ Terms : $-4\mathrm{x},5\mathrm{y}$ Factors:-4, x ; 5, y (c) $5y+3y^2$ Terms:5y, 3y ${}^2$ Factors: 5, y; 3, y, y (d) $xy+2x^2{y}^2$ Terms: $xy,2x^2{y}^2$ Factors: $\mathrm{x},\mathrm{y};2,\mathrm{x},\mathrm{x},\mathrm{y},\mathrm{y}$ (e) $pq+q$ Terms : pq, q Factors: p, q; q (f) $1.2\mathrm{ab}-2.4\mathrm{b}+3.6\mathrm{a}$ Terms : 1.2ab, $-2.4\mathrm{b},3.6\mathrm{a}$ Factors : 1.2, a, b;-2.4, b; 3.6, a (g) $\frac{3}{4}x+\frac{1}{4}$ Terms : $\frac{3}{4}\mathrm{x},\frac{1}{4}$ Factors: $\frac{3}{4},\mathrm{x};\frac{1}{4}$ (h) $0.1p^2+0.2q^2$ Terms: $0.1{\mathrm{p}}^2,0.2{\mathrm{q}}^2$ Factors: 0.1, p, p; 0.2, q, q
• Identify the numerical coefficients of terms (other than constants) in the following expressions. (i) $5-3t^2$ (ii) $1+t+t^2+t^3$ (iii) $x+2xy+3y$ (iv) $100m+1000n$ (v) $-p^2{q}^2+7pq$ (vi) $1.2\mathrm{a}+0.8\mathrm{b}$ (vii) $3.14{\mathrm{r}}^2$ (viii) $2(\ell +b)$ (ix) $0.1y+0.01{\mathrm{y}}^2$ Sol.

• (a) Identify terms which contain $x$ and give the coefficient of $x$. (i) $y^{2}x+y$ (ii) $13y^2-8yx$ (iii) $x+y+2$ (iv) $5+\mathrm{z}+\mathrm{zx}$ (v) $1+x+xy$ (vi) $12{\mathrm{xy}}^2+25$ (vii) $7x+x{y}^2$ (b) Identify terms which contain ${\mathrm{y}}^2$ and give the coefficient of $y^2$. (i) $8-x{y}^2$ (ii) $5y^2+7x$ (iii) $2x^{2}y-15x{y}^2+7y^2$ Sol. (a)

• (b)

• Classify into monomials, binomials and trinomials. (i) $4y-7z$ (ii) ${\mathrm{y}}^2$ (iii) $x+y-xy$ (iv) 100 (v) $ab-a-b$ (vi) $5-3\mathrm{t}$ (vii) $4p^{2}q-4p^2$ (viii) 7 mn (ix) $z^2-3z+8$ (x) ${\mathrm{a}}^2+{\mathrm{b}}^2$ (xi) $z^2+z$ (xii) $1+\mathrm{x}+{\mathrm{x}}^2$ Sol.

• State whether a given pair of terms is of like or unlike terms. (i) 1,100 (ii) $-7x,\frac{5}{2}x$ (iii) $-29\mathrm{x},-29\mathrm{y}$ (iv) $14\mathrm{xy},42\mathrm{yx}$ (v) $4{\mathrm{m}}^2\mathrm{p},4{\mathrm{mp}}^2$ (vi) $12xz,12x^2{z}^2$ Sol.

• Identify like terms in the following : (a) $-x{y}^2,-4y{x}^2,8x^2,2x{y}^2,7y,-11x^2$, $-100x,-11yx,20x^{2}y,-6x^2,y,2xy,3x$ (b) $10pq,7p,8q,-p^2{q}^2,-7qp,-100q,-23$, $12q^2{p}^2,-5p^2,41,2405p,78qp,13p^{2}q$, qp ${}^2,701p^2$ Sol. (a) Like terms are: (i) $-x{y}^2,2x{y}^2$ (ii) $-4y{x}^2,20x^{2}y$ (iii) $8x^2,-11x^2,-6x^2$ (iv) $7\mathrm{y},\mathrm{y}$ (v) $-100x,3x$ (vi) - $11\mathrm{yx},2\mathrm{xy}$ (b) Like terms are: (i) $10\mathrm{pq},-7\mathrm{pq},78\mathrm{pq}$ (ii) $7\mathrm{p},2405\mathrm{p}$ (iii) $8q,-100q$ (iv) $-p^2{q}^2,12p^2{q}^2$ (v) $-23,41$ (vi) $-5p^2,701p^2$ (vii) $13{\mathrm{p}}^2\mathrm{q},{\mathrm{qp}}^2$

Exercise: 10.2

• If $m=2$, find the value of (i) $\mathrm{m}-2$ (ii) $3m-5$ (iii) $9-5m$ (iv) $3m^2-2m-7$ (v) $\frac{5m}{2}-4$ Sol. (i) $\mathrm{m}-2=2-2=0[$ Putting $\mathrm{m}=2]$ (ii) $3\mathrm{m}-5=3\times 2-5$ [Putting $\mathrm{m}=2$ ] $=6-5=1$ (iii) $9-5\mathrm{m}=9-5\times 2$ [Putting $\mathrm{m}=2$ ] $=9-10=-1$ (iv) $3m^2-2m-7$ [Putting $m=2]$ $=3(2{)}^2-2(2)-7$ $=3\times 4-2\times 2-7=12-4-7$ $=12-11=1$ (v) $\frac{5\mathrm{m}}{2}-4=\frac{5\times 2}{2}-4$ [Putting $\mathrm{m}=2$ ] $=5-4=1$
• If $p=-2$, find the value of : (i) $4p+7$ (ii) $-3p^2+4p+7$ (iii) $-2p^3-3p^2+4p+7$ Sol. (i) $4p+7=4(-2)+7[$ Putting $p=-2]$ $=-8+7=-1$ (ii) $-3p^2+4p+7[$ Putting $p=-2]$ $=-3(-2{)}^2+4(-2)+7$ $=-3\times 4-8+7=-12-8+7$ $=-20+7=-13$ (iii) $-2p^3-3p^2+4p+7[$ Putting $p=-2]$ $=-2(-2{)}^3-3(-2{)}^2+4(-2)+7$ $=-2\times (-8)-3\times 4-8+7=16-12-8+7$ $=-20+23=3$
• Find the value of the following expressions, when $x=-1$ : (i) $2\mathrm{x}-7$ (ii) $-x+2$ (iii) $x^2+2x+1$ (iv) $2x^2-x-2$ Sol. (i) $2\mathrm{x}-7=2(-1)-7$ [Putting $\mathrm{p}=-1$ ] $=-2-7=-9$ (ii) $-\mathrm{x}+2=-(-1)+2$ [Putting $\mathrm{p}=-1]$ $=1+2=3$ (iii) ${\mathrm{x}}^2+2\mathrm{x}+1$ [Putting $\mathrm{p}=-1]$ $=(-1{)}^2+2(-1)+1$ $=1-2+1=2-2=0$ (iv) $2x^2-x-2$ [Putting $p=-1]$ $=2(-1{)}^2-(-1)-2$ $=2\times 1+1-2=2+1-2$ $=3-2=1$
• If $a=2,b=-2$, find the value of: (i) $a^2+b^2$ (ii) $a^2+b^2+ab$ (iii) $a^2-b^2$ Sol. (i) ${\mathrm{a}}^2+{\mathrm{b}}^2=(2{)}^2+(-2{)}^2[$ Putting $\mathrm{a}=2,\mathrm{b}=-2]$ $=4+4$ $=8$ (ii) ${\mathrm{a}}^2+\mathrm{ab}+{\mathrm{b}}^2$ $=(2{)}^2+(2)(-2)+(-2{)}^2$ [Putting a $=2,\mathrm{b}=-2$ ] $=4-4+4$ $=4$ (iii) ${\mathrm{a}}^2-{\mathrm{b}}^2=(2{)}^2-(-2{)}^2[$ Putting $a=2,\mathrm{b}=2]$ $=4-4$ $=0$
• When $\mathrm{a}=0,\mathrm{b}=-1$, find the value of the given expressions : (i) $2a+2b$ (ii) $2a^2+b^2+1$ (iii) $2a^{2}b+2a{b}^2+ab$ (iv) $a^2+ab+2$ Sol. (i) $2\mathrm{a}+2\mathrm{b}=2(0)+2(-1)$ [Putting $a=0,b=-1$ ] $=0-2=-2$ (ii) $2{\mathrm{a}}^2+{\mathrm{b}}^2+1$ $=2(0{)}^2+(-1{)}^2+1$ [Putting $a=0,b=1]$ $=2\times 0+1+1=0+2=2$ (iii) $2{\mathrm{a}}^2\mathrm{b}+2{\mathrm{ab}}^2+\mathrm{ab}[$ Putting $\mathrm{a}=0,\mathrm{b}=-1]$ $=2(0{)}^2(-1)+2(0)(-1{)}^2+(0)(-1)$ $=0+0+0=0$ (iv) $a^2+ab+2$ $=(0{)}^2+(0)(-1)+2[$ Puttinga $=0,b=-1]$ $=0+0+2=2$
• Simplify the expression and find the value if $x$ is equal to 2 (i) $\mathrm{x}+7+4(\mathrm{x}-5)$ (ii) $3(x+2)+5x-7$ (iii) $6x+5(x-2)$ (iv) $4(2x-1)+3x+11$ Sol. (i) $x+7+4(x-5)=x+7+4x-20$ $=x+4\mathrm{x}+7-20=5\mathrm{x}-13$ $=5\times 2-13$ [Putting $\mathrm{x}=2$ ] $=10-13=-3$ (ii) $3(x+2)+5x-7=3x+6+5x-7$ $=3x+5x+6-7=8x-1$ $=8\times 2-1[$ Putting $x=2]$ $=16-1=15$ (iii) $6x+5(x-2)=6x+5x-10$ $=11\mathrm{x}-10$ $=11\times 2-10[$ Putting $\mathrm{x}=2]$ $=22-10=12$ (iv) $4(2x-1)+3x+11=8x-4+3x+11$ $=8\mathrm{x}+3\mathrm{x}-4+11=11\mathrm{x}+7$ $=11\times 2+7$ [Putting $\mathrm{x}=2$ ] $=22+7=29$
• Simplify these expressions and find their values if $\mathrm{x}=3,\mathrm{a}=-1,\mathrm{b}=-2$. (i) $3x-5-x+9$ (ii) $2-8\mathrm{x}+4\mathrm{x}+4$ (iii) $3a+5-8a+1$ (iv) $10-3b-4-5b$ (v) $2a-2b-4-5+a$ Sol. (i) $3x-5-x+9=3x-x-5+9=2x+4$ $=2\times 3+4$ [Putting $x=3$ ] $=6+4=10$ (ii) $2-8\mathrm{x}+4\mathrm{x}+4=-8\mathrm{x}+4\mathrm{x}+2+4$ $=-4x+6$ [Putting $x=3$ ] $=-4\times 3+6=-12+6=-6$ (iii) $3a+5-8a+1=3a-8a+5+1=-5a+6$ $=-5(-1)+6[$ Putting $a=-1]$ $=5+6=11$ (iv) $10-3b-4-5b=-3b-5b+10-4$ $=-8b+6=-8(-2)+6$ [Putting $\mathrm{b}=-2$ ] $=16+6=22$ (v) $2\mathrm{a}-2\mathrm{b}-4-5+\mathrm{a}=2\mathrm{a}+\mathrm{a}-2\mathrm{b}-4-5$ $=3a-2b-9$ [Putting $a=-1,b=-2]$ $=3(-1)-2(-2)-9=-3+4-9=-8$
• (i) If $z=10$, find the value of $z^3-3(z-10)$. (ii) If $p=-10$, find the value of $p^2-2p-100$ Sol. (i) $z^3-3(z-10)$ $=(10{)}^3-3(10-10)$ [Putting $\mathrm{z}=10$ ] $=1000-3\times 0=1000-0=1000$ (ii) ${\mathrm{p}}^2-2\mathrm{p}-100$ [Putting $\mathrm{p}=-10]$ $=(-10{)}^2-2(-10)-100$ $=100+20-100=20$
• What should be the value of a if the value of $2x^2+x-$ a equals to 5 , when $x=0$ ? Sol. Given: $2x^2+x-a=5$ $\Rightarrow 2(0{)}^2+0-\mathrm{a}=5[$ Putting $\mathrm{x}=0]$ $\Rightarrow 0+0-\mathrm{a}=5\Rightarrow \mathrm{a}=-5$ Hence, the value of a is -5 .
• Simplify the expression and find its value when $\mathrm{a}=5$ and $\mathrm{b}=-3.2\left({\mathrm{a}}^2+\mathrm{ab}\right)+3-\mathrm{ab}$ Sol. Given: $2\left(a^2+ab\right)+3-ab$ $\Rightarrow 2{\mathrm{a}}^2+2\mathrm{ab}+3-\mathrm{ab}$ $\Rightarrow 2{\mathrm{a}}^2+2\mathrm{ab}-\mathrm{ab}+3$ $\Rightarrow 2{\mathrm{a}}^2+\mathrm{ab}+3$ $\Rightarrow 2(5{)}^2+(5)(-3)+3[$ Putting $a=5,b=-3]$ $\Rightarrow 2\times 25-15+3$ $\Rightarrow 50-15+3\Rightarrow 38$

Answer Key

Multiple choice questions

True or False

• False
• False
• True
• False
• False

Fill in the blanks

• monomial
• numerical
• $\frac{-2}{3}{x}^2$
• -4 x
• $-2(a+b+c)$
• $3x-2$
• unlike
• subtracted
• 5
• 1
• $-4,\mathrm{x},\mathrm{x},\mathrm{y}$
• $x^3-y^3$
• 25 kg
• 5, 0
• $\frac{1}{2}pq$

Exercise-02

Very short answer type questions

• Write down the numerical as well as the literal coefficient of each of the following monomials: (i) $-10x^{2}y$ (ii) $\frac{6}{13}{a}^{2}bc$ (iii) $-\frac{5}{9}$ abc (iv) -pq (v) $-\frac{5xy}{9z}$ (vi) $-8x^2{y}^2{z}^2$
• Group the like terms together. (i) $6\mathrm{a},5\mathrm{b},-7\mathrm{a},-3\mathrm{b}$ (ii) $11\mathrm{x},-3\mathrm{y},6\mathrm{y},\mathrm{y},8\mathrm{x},-6\mathrm{x}$ and 5 x (iii) $6m,8mn,-16mn,-10m,-8m^2,15m^2$ and 14 mn (iv) $14x^{2}y,2x{y}^2,6xy,-6yx,5y{x}^2$ and $14y^{2}x$
• Identify the type of algebraic expression and state the degree of each. (i) $3-8x$ (ii) $x^2+4y^2$ (iii) $8x^2{y}^6+x^5$ (iv) $-6a^3+5a^{3}b-a{b}^3+9b^4$ (v) $6a^3-2a^2{b}^2+18a^4-16a^3{b}^4-22a^6+16b^8$ (vi) $18a^4{b}^3-6a^3{b}^6+20a^7-16b^8+20a^4{b}^4$
• Identify polynomials from the given algebraic expressions. (i) $\frac{4}{9}{x}^2-\frac{4}{9}{x}^2+4$ (ii) $\frac{2}{\mathrm{x}}+\frac{3}{{\mathrm{x}}^2}-4{\mathrm{x}}^2+3\mathrm{x}+2$ (iii) $3a^3+4a^{2}b+8b^3$ (iv) ${\mathrm{x}}^2-\frac{1}{{\mathrm{x}}^2}+2$
• Add the following: (i) $-3p+6q,3p-3q$ (ii) $8p-6q,3p-4q,12q-12p$ (iii) $6\mathrm{x}-4\mathrm{y}-2\mathrm{z},3\mathrm{y}-2\mathrm{x}+\mathrm{z},4\mathrm{z}-\mathrm{x}-2\mathrm{y}$ (iv) $15p^2+10pq-6q^2,-8pq+10p^2-9q^2$
• Subtract the first expression from the second. (i) 16a, 18a (ii) $-12\mathrm{x},10$ (iii) $-4bc,12$

Short answer type questions

• Add the following: (i) $5a^2+8a-4,3a^2-4a+11,-4a^2-3a+6$ (ii) ${\mathrm{p}}^2+{\mathrm{q}}^2+2\mathrm{pq},3{\mathrm{p}}^2+3{\mathrm{r}}^2+6\mathrm{pr},9{\mathrm{r}}^2-4{\mathrm{p}}^2+6\mathrm{pr}$ (iii) $a^{2}b+a{b}^2-abc-b^{2}c,5a^{2}b-6a{b}^2-3abc-2c{b}^2$ (iv) $\frac{2}{5}x-\frac{3}{2}y+2z,\frac{x}{3}+\frac{y}{4}-\frac{z}{2}$ and $\frac{-4\mathrm{x}}{5}+\frac{\mathrm{y}}{3}-\frac{3\mathrm{z}}{2}$ (v) $\frac{5x^2}{3}-\frac{7x}{2}+11,\frac{7x^2}{2}+\frac{5x}{3}-6$ and $\frac{7x^2}{3}-\frac{4x}{3}-2$ (vi) $2-\frac{2}{5}{x}^3+3x^2,x^3-\frac{x^2}{4}+5$ and $\frac{2x^3}{5}+$ $\frac{3x^2}{4}-10$
• Subtract the first expression from the second. (i) $8{\mathrm{p}}^2-6{\mathrm{p}}^2\mathrm{q}+8{\mathrm{q}}^2,12{\mathrm{p}}^2-16{\mathrm{p}}^2\mathrm{q}+8{\mathrm{pq}}^2+9{\mathrm{q}}^2$ (ii) $9p^3+4p^2+6p-4,12p^3-12$ (iii) $6a^4-2a^2{b}^2+2b^4,8a^4-6a^2{b}^2+8a^{3}b-$ $8a^{2}b-b^4$ (iv) $\frac{6x^2}{5}-\frac{2x}{3}+10,\frac{8x^2}{3}-\frac{3x}{2}+8$ (v) $\frac{5x^2}{2}-\frac{2y^2}{3}+\frac{xy}{6},\frac{3x^2}{2}-\frac{3y^2}{4}+\frac{xy}{6}$
• Subtract: (i) $9a^2+19b+21$ from $12a^2+26b+32$. (ii) Add $8p+3q+9$ to the difference of $16p+5q+10$ and $6p-3q-1$. (iii) Subtract the sum of $2a+3b+7$ and $9a-3b-5$ from the sum of $7a+3b+9$ and $6a+5b+1$ (iv) What must be added to $3x^3+5x-x^2-5$ to get $2x^2-2x-2x^3+2$ ? (v) What must be subtracted from $6p^3+$ $6p-p^2-7$ to get $-6p^2+8-2p$ ?

Long answer type questions

• Draw a tree diagram for each of the following expressions. (i) $2\mathrm{a}+4\mathrm{b}$ (ii) $-7a^2+15ab$ (iii) $4x^2{y}^3+6x$
• Find the product: (i) $3x\left(x^2-2x\right)$ (ii) $2xy\left(x^2-y^2\right)$ (iii) $-3xy\left(x^{2}y-2x{y}^2\right)$ (iv) $\frac{xy}{5}(-2x-5y)$ (v) $(4abc+3ab)\times \left(-4b^{2}c\right)$ (vi) $(2a-6b)(a+4b)$ (vii) $(2x-3y)\left(4x^2+6xy+9y^2\right)$ (viii) $(a-3b+5)(2a+2b-6)$ (ix) $\left(x^3-x^2-x-5\right)\left(x^3+x^2+x+5\right)$ (x) $\left(a^3+a^2+a+2\right)\left(a^3-a^2-a-2\right)$ (xi) $\left(\frac{3x}{7}+\frac{2y}{3}\right)\left(\frac{3x}{7}-\frac{2y}{3}\right)$ (xii) $\left(\frac{x}{2}-\frac{3y}{5}\right)(2x+5y)$
• Find the value of the following expressions if $\mathrm{a}=1,\mathrm{b}=-1$. (i) ${\mathrm{a}}^2-{\mathrm{b}}^2$ (ii) ${\mathrm{a}}^2+3ab+{\mathrm{b}}^2$ (iii) $3a^4-2b^3-a$
• By how much is sum of $a^4-6a^2{b}^2+b^4$ and $-2a^4+5a^2{b}^2+3b^4$ greater than $-a^4-a^2{b}^2-4b^4$ ?
• From the sum of $4+3x$ and $5-4x+2x^2$, subtract the sum of $3x^2-5x$ and $-x^2+2x+5$ and write the degree of the difference obtained.
• If $4a-3=13$, then find the value of $10a^2-5a+6$.
• If $\Vert \Vert \Vert +\equiv +$represents $4x^2+3y^2+z$, then write the algebraic expression for $\equiv +\square \square \square +\mid$.
• Fill in the blanks to make the given addition sentence true: $6a{b}^3+\dots ..+2b^{2}c+8abc-14b^{3}a=15b^{2}c$ $+....+20abc-12abc$
• What values of $a$ and $b$ make the given statement true? $\left(a{y}^2+3xy-9x^2\right)-\left(-4y^2+8xy+b{x}^2\right)$ $=10y^2-5xy-10x^2$
• If $2x-2=4$ and $0.05y=0.15$, find the value of $y^2-x^2$.
• Find the area of a rectangle whose length and breadth is $(x+2y)\mathrm{cm}$ and $(3x-2y)cm$ respectively.

Answer Key

Very short answer type questions

• (i) $-10,x^{2}y$ (ii) $\frac{6}{13},a^{2}bc$ (iii) $\frac{-5}{9}$,abc (iv) $-1,\mathrm{pq}$ (v) $\frac{-5}{9},\frac{xy}{z}$ (vi) $-8,x^2{y}^2{z}^2$
• (i) $(6a,-7a),(5b,-3b)$ (ii) $(11x,8x,-6x,5x),(-3y,6y,y)$ (iii) $(6m,-10m),(8mn,-16mn,14mn),\left(-8m^2,15m^2\right)$ (iv) $\left(14x^{2}y,5y{x}^2\right),(6xy,-6yx),\left(2x{y}^2,14y^{2}x\right)$

(i) Binomial, 1 (ii) Binomial, 2 (iii) Binomial, 8 (iv) Quadrinomial, 4 (v) Multinomial, 8 (vi) Multinomial, 9

• (i) and (iii) are polynomials.

(i) 3 q (ii) $2\mathrm{q}-\mathrm{p}$ (iii) $3x-3y+3z$ (iv) $25p^2+2pq-15q^2$ (ii) $10+12\mathrm{x}$ (iii) $12+4bc$

• (i) $2a$

Short answer type questions

• (i) $4a^2+a+13$ (ii) $q^2+2pq+12r^2+12pr$ (iii) $6a^{2}b-5a{b}^2-4abc-3b^{2}c$ (iv) $\frac{-\mathrm{x}}{15}-\frac{11\mathrm{y}}{12}$ (v) $\frac{15x^2}{2}-\frac{19x}{6}+3$ (vi) $\left(x^3+\frac{7x^2}{2}-3\right)$
• (i) $4p^2-10p^{2}q+8p{q}^2+q^2$ (ii) $3p^3-4p^2-6p-8$ (iii) $2a^4-4a^2{b}^2+8a^{3}b-8a^{2}b-3b^4$ (iv) $\frac{22}{15}{x}^2-\frac{5}{6}x-2$ (v) $-x^2-\frac{1}{12}{y}^2$

(i) $3a^2+7b+11$ (ii) $18p+11q+20$ (iii) $2\mathrm{a}+8\mathrm{b}+8$ (iv) $-5x^3-7x+3x^2+7$ (v) $6p^3+8p+5p^2-15$

Long answer type questions

• (i)

• (iii) Terms Factors

• (ii)
• (i) $3x^3-6x^2$ (ii) $2x^{3}y-2x{y}^3$ (iii) $-3x^3{y}^2+6x^2{y}^3$ (iv) $\frac{-2}{5}{x}^{2}y-x{y}^2$ (v) $-16{\mathrm{ab}}^3{\mathrm{c}}^2-12{\mathrm{ab}}^3\mathrm{c}$ (vi) $2{\mathrm{a}}^2+2\mathrm{ab}-24{\mathrm{b}}^2$ (vii) $8x^3-27y^3$ (viii) $2a^2-6b^2-4ab+4a+28b-30$ (ix) $x^6-x^4-2x^3-11x^2-10x-25$ (x) $a^6-a^4-2a^3-5a^2-4a-4$ (xi) $\frac{9}{49}{x}^2-\frac{4}{9}{y}^2$ (xii) $x^2-3y^2+\frac{13}{10}xy$
• (i) 0 (ii) -1 (iii) 4
• $+8b^4$
• $4+2x$, degree $=1$
• 146
• $4y^2+3z+x^2$
• $13b^{2}c,-8a{b}^3$
• $a=6,b=1$
• 0
• $\left(3x^2+4xy-4y^2\right)c{m}^2$