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
NCERT Solutions for Class 7 Maths Chapter 10: Algebraic Expressions
2.0Key Concepts in Class 7 Maths Chapter 10: Algebraic Expressions
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
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.
Coefficients:
The numerical factor of a term.
Example: In 5x², the coefficient of x² is 5.
Variables:
Letters that represent unknown quantities.
Example: x, y, a, b in the above expressions.
Constants:
Numbers that have a fixed value.
Example: 3, 5, -2 in the above expressions.
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
Addition and Subtraction of Algebraic Expressions:
Rule: Only like terms can be added or subtracted.
Example:
3x + 5x = 8x
7y² - 2y² = 5y²
Multiplication of Algebraic Expressions:
Use the distributive law: a(b + c) = ab + ac
Multiply monomials, binomials, and polynomials using appropriate rules.
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) 2x+y
(iii) z2
(iv) 4pq
(v) x2+y2
(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+x2
(c) y−y3
(d) 5xy2+7x2y
(e) −ab+2b2−3a2
(ii) Identify terms and factors in the expressions given below :
(a) −4x+5
(b) −4x+5y
(c) 5y+3y2
(d) xy+2x2y2
(e) pq+q
(f) 1.2ab−2.4b+3.6a
(g) 43x+41
(h) 0.1p2+0.2q2
Sol.(i) (a) x−3
Expression
Terms
Factors
(b) 1+x+x2
Expression
Terms
(c) y−y3
Expression
Terms
Factors
(d) 5xy2+7x2y Expression Terms Factors
(e) −ab+2b2−3a2
Expression
Terms
Factors
(ii) (a) −4x+5
Terms: −4x,5
Factors: −4,x;5
(b) −4x+5y
Terms : −4x,5y
Factors:-4, x ; 5, y
(c) 5y+3y2
Terms:5y, 3y 2
Factors: 5, y; 3, y, y
(d) xy+2x2y2
Terms: xy,2x2y2
Factors: x,y;2,x,x,y,y
(e) pq+q
Terms : pq, q
Factors: p, q; q
(f) 1.2ab−2.4b+3.6a
Terms : 1.2ab, −2.4b,3.6a
Factors : 1.2, a, b;-2.4, b; 3.6, a
(g) 43x+41
Terms : 43x,41
Factors: 43,x;41
(h) 0.1p2+0.2q2
Terms: 0.1p2,0.2q2
Factors: 0.1, p, p; 0.2, q, q
Identify the numerical coefficients of terms (other than constants) in the following expressions.
(i) 5−3t2
(ii) 1+t+t2+t3
(iii) x+2xy+3y
(iv) 100m+1000n
(v) −p2q2+7pq
(vi) 1.2a+0.8b
(vii) 3.14r2
(viii) 2(ℓ+b)
(ix) 0.1y+0.01y2
Sol.
(a) Identify terms which contain x and give the coefficient of x.
(i) y2x+y
(ii) 13y2−8yx
(iii) x+y+2
(iv) 5+z+zx
(v) 1+x+xy
(vi) 12xy2+25
(vii) 7x+xy2(b) Identify terms which contain y2 and give the coefficient of y2.
(i) 8−xy2
(ii) 5y2+7x
(iii) 2x2y−15xy2+7y2
Sol. (a)
State whether a given pair of terms is of like or unlike terms.
(i) 1,100
(ii) −7x,25x
(iii) −29x,−29y
(iv) 14xy,42yx
(v) 4m2p,4mp2
(vi) 12xz,12x2z2
Sol.
S.No.
Pair of terms
Like / Unlike terms
(i)
1,100
Like terms
(ii)
−7x,25x
Like terms
(iii)
−29x,−29y
Unlike terms
(iv)
14xy,42yx
Like terms
(v)
4m2p,4mp2
Unlike terms
(vi)
12xz,12x2z2
Unlike terms
Identify like terms in the following :
(a) −xy2,−4yx2,8x2,2xy2,7y,−11x2, −100x,−11yx,20x2y,−6x2,y,2xy,3x
(b) 10pq,7p,8q,−p2q2,−7qp,−100q,−23, 12q2p2,−5p2,41,2405p,78qp,13p2q, qp 2,701p2
Sol. (a) Like terms are:
(i) −xy2,2xy2
(ii) −4yx2,20x2y
(iii) 8x2,−11x2,−6x2
(iv) 7y,y
(v) −100x,3x
(vi) - 11yx,2xy
(b) Like terms are:
(i) 10pq,−7pq,78pq
(ii) 7p,2405p
(iii) 8q,−100q
(iv) −p2q2,12p2q2
(v) −23,41
(vi) −5p2,701p2
(vii) 13p2q,qp2
Exercise: 10.2
If m=2, find the value of
(i) m−2
(ii) 3m−5
(iii) 9−5m
(iv) 3m2−2m−7
(v) 25m−4
Sol. (i) m−2=2−2=0[ Putting m=2]
(ii) 3m−5=3×2−5 [Putting m=2 ]
=6−5=1
(iii) 9−5m=9−5×2 [Putting m=2 ] =9−10=−1
(iv) 3m2−2m−7 [Putting m=2]=3(2)2−2(2)−7=3×4−2×2−7=12−4−7=12−11=1
(v) 25m−4=25×2−4 [Putting m=2 ]
=5−4=1
If p=−2, find the value of :
(i) 4p+7
(ii) −3p2+4p+7
(iii) −2p3−3p2+4p+7
Sol. (i) 4p+7=4(−2)+7[ Putting p=−2]=−8+7=−1
(ii) −3p2+4p+7[ Putting p=−2]=−3(−2)2+4(−2)+7=−3×4−8+7=−12−8+7=−20+7=−13
(iii) −2p3−3p2+4p+7[ Putting p=−2]=−2(−2)3−3(−2)2+4(−2)+7=−2×(−8)−3×4−8+7=16−12−8+7=−20+23=3
Find the value of the following expressions, when x=−1 :
(i) 2x−7
(ii) −x+2
(iii) x2+2x+1
(iv) 2x2−x−2
Sol. (i) 2x−7=2(−1)−7 [Putting p=−1 ] =−2−7=−9
(ii) −x+2=−(−1)+2 [Putting p=−1]=1+2=3
(iii) x2+2x+1 [Putting p=−1]=(−1)2+2(−1)+1=1−2+1=2−2=0
(iv) 2x2−x−2 [Putting p=−1]=2(−1)2−(−1)−2=2×1+1−2=2+1−2=3−2=1
If a=2,b=−2, find the value of:
(i) a2+b2
(ii) a2+b2+ab
(iii) a2−b2
Sol. (i) a2+b2=(2)2+(−2)2[ Putting a=2,b=−2]=4+4=8
(ii) a2+ab+b2=(2)2+(2)(−2)+(−2)2
[Putting a =2,b=−2 ]
=4−4+4=4
(iii) a2−b2=(2)2−(−2)2[ Putting a=2,b=2]=4−4=0
When a=0,b=−1, find the value of the given expressions :
(i) 2a+2b
(ii) 2a2+b2+1
(iii) 2a2b+2ab2+ab
(iv) a2+ab+2
Sol. (i) 2a+2b=2(0)+2(−1)
[Putting a=0,b=−1 ]
=0−2=−2
(ii) 2a2+b2+1=2(0)2+(−1)2+1 [Putting a=0,b=1]=2×0+1+1=0+2=2
(iii) 2a2b+2ab2+ab[ Putting a=0,b=−1]=2(0)2(−1)+2(0)(−1)2+(0)(−1)=0+0+0=0
(iv) a2+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) x+7+4(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+4x+7−20=5x−13=5×2−13 [Putting x=2 ]
=10−13=−3
(ii) 3(x+2)+5x−7=3x+6+5x−7=3x+5x+6−7=8x−1=8×2−1[ Putting x=2]=16−1=15
(iii) 6x+5(x−2)=6x+5x−10=11x−10=11×2−10[ Putting x=2]=22−10=12
(iv) 4(2x−1)+3x+11=8x−4+3x+11=8x+3x−4+11=11x+7=11×2+7 [Putting x=2 ]
=22+7=29
Simplify these expressions and find their values if x=3,a=−1,b=−2.
(i) 3x−5−x+9
(ii) 2−8x+4x+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=2×3+4
[Putting x=3 ]
=6+4=10
(ii) 2−8x+4x+4=−8x+4x+2+4=−4x+6
[Putting x=3 ]
=−4×3+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 b=−2 ]
=16+6=22
(v) 2a−2b−4−5+a=2a+a−2b−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 z3−3(z−10).
(ii) If p=−10, find the value of p2−2p−100
Sol. (i) z3−3(z−10)=(10)3−3(10−10) [Putting z=10 ]
=1000−3×0=1000−0=1000
(ii) p2−2p−100 [Putting p=−10]=(−10)2−2(−10)−100=100+20−100=20
What should be the value of a if the value of 2x2+x− a equals to 5 , when x=0 ?
Sol. Given: 2x2+x−a=5⇒2(0)2+0−a=5[ Putting x=0]⇒0+0−a=5⇒a=−5
Hence, the value of a is -5 .
Simplify the expression and find its value when a=5 and b=−3.2(a2+ab)+3−ab
Sol. Given: 2(a2+ab)+3−ab⇒2a2+2ab+3−ab⇒2a2+2ab−ab+3⇒2a2+ab+3⇒2(5)2+(5)(−3)+3[ Putting a=5,b=−3]⇒2×25−15+3⇒50−15+3⇒38
Answer Key
Multiple choice questions
Question
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Answer
3
2
2
2
4
2
2
3
3
1
4
2
2
3
4
Question
16
17
18
19
20
Answer
2
4
4
4
1
True or False
False
False
True
False
False
Fill in the blanks
monomial
numerical
3−2x2
-4 x
−2(a+b+c)
3x−2
unlike
subtracted
5
1
−4,x,x,y
x3−y3
25 kg
5, 0
21pq
Exercise-02
Very short answer type questions
Write down the numerical as well as the literal coefficient of each of the following monomials:
(i) −10x2y
(ii) 136a2bc
(iii) −95 abc
(iv) -pq
(v) −9z5xy
(vi) −8x2y2z2
Group the like terms together.
(i) 6a,5b,−7a,−3b
(ii) 11x,−3y,6y,y,8x,−6x and 5 x
(iii) 6m,8mn,−16mn,−10m,−8m2,15m2 and 14 mn
(iv) 14x2y,2xy2,6xy,−6yx,5yx2 and 14y2x
Identify the type of algebraic expression and state the degree of each.
(i) 3−8x
(ii) x2+4y2
(iii) 8x2y6+x5
(iv) −6a3+5a3b−ab3+9b4
(v) 6a3−2a2b2+18a4−16a3b4−22a6+16b8
(vi) 18a4b3−6a3b6+20a7−16b8+20a4b4
Identify polynomials from the given algebraic expressions.
(i) 94x2−94x2+4
(ii) x2+x23−4x2+3x+2
(iii) 3a3+4a2b+8b3
(iv) x2−x21+2
Add the following:
(i) −3p+6q,3p−3q
(ii) 8p−6q,3p−4q,12q−12p
(iii) 6x−4y−2z,3y−2x+z,4z−x−2y
(iv) 15p2+10pq−6q2,−8pq+10p2−9q2
Subtract the first expression from the second.
(i) 16a, 18a
(ii) −12x,10
(iii) −4bc,12
Short answer type questions
Add the following:
(i) 5a2+8a−4,3a2−4a+11,−4a2−3a+6
(ii) p2+q2+2pq,3p2+3r2+6pr,9r2−4p2+6pr
(iii) a2b+ab2−abc−b2c,5a2b−6ab2−3abc−2cb2
(iv) 52x−23y+2z,3x+4y−2z and 5−4x+3y−23z
(v) 35x2−27x+11,27x2+35x−6 and 37x2−34x−2
(vi) 2−52x3+3x2,x3−4x2+5 and 52x3+43x2−10
Subtract the first expression from the second.
(i) 8p2−6p2q+8q2,12p2−16p2q+8pq2+9q2
(ii) 9p3+4p2+6p−4,12p3−12
(iii) 6a4−2a2b2+2b4,8a4−6a2b2+8a3b−8a2b−b4
(iv) 56x2−32x+10,38x2−23x+8
(v) 25x2−32y2+6xy,23x2−43y2+6xy
Subtract:
(i) 9a2+19b+21 from 12a2+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 3x3+5x−x2−5 to get 2x2−2x−2x3+2 ?
(v) What must be subtracted from 6p3+6p−p2−7 to get −6p2+8−2p ?
Long answer type questions
Draw a tree diagram for each of the following expressions.
(i) 2a+4b
(ii) −7a2+15ab
(iii) 4x2y3+6x
4.0Benefits of NCERT Solutions for Class 7 Maths Chapter 10
The chapter introduces core algebraic concepts like variables, constants, terms, coefficients, and expressions. These are building blocks for higher-level algebra and other branches of mathematics.
NCERT Solutions breaks down these concepts into easy-to-understand explanations, ensuring a solid foundation for students.
The solutions guide students through adding and subtracting algebraic expressions, including combining like terms and simplifying expressions.
Students learn how to multiply monomials, binomials, and polynomials and divide monomials by monomials.
Important algebraic identities are introduced and explained, providing valuable shortcuts for solving algebraic problems.
Algebraic expressions are used in various real-world situations. NCERT Solutions can help students understand how algebraic concepts are applied in everyday life, making learning more engaging.
5.0Why are NCERT Solutions for Class 7 Maths Chapter 10 important?
Foundation for Higher Mathematics: These concepts are fundamental to understanding more advanced algebraic topics like equations, inequalities, and functions.
Problem-Solving: They are essential for solving various mathematical problems in algebra and other areas of mathematics.
Real-World Applications: Algebraic expressions are used to model and solve real-world problems in various fields, such as physics, engineering, and economics.
NCERT Solutions for Class 7 Maths Other Chapters:-
An algebraic expression is a combination of variables, constants and mathematical operations. For examples: 10x + 5, 2a - c
Like Terms: Terms with the same variables and exponents (e.g., 3x and 7x). Unlike Terms: Terms with different variables or exponents (e.g., 3x and 5y).
Only like terms can be added or subtracted.
NCERT Solutions for Class 7 Maths Chapter 10 is helpful for Clear explanations, solving practice problems, building a strong foundation and exam preparation.