NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2

NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2 helps students learn how to add and subtract algebraic expressions. This exercise builds on the basics introduced earlier and focuses on combining like terms. Through simple examples and clear steps, students understand how to handle terms with variables and constants correctly.

These NCERT Solutions are written in an easy-to-understand format and follow the latest NCERT syllabus. Practicing NCERT Solutions from this exercise improves students' confidence in solving algebraic expressions and prepares them well for upcoming topics.

1.0Download NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2: Free PDF

Download the free NCERT Solutions Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.2 PDF with clear steps to help you solve problems easily and score better.

2.0Key Concepts in Exercise 8.2 of Class 8 Maths Chapter 8

Exercise 8.2 focuses on the addition and subtraction of algebraic expressions, helping students learn how to combine and simplify expressions with like and unlike terms. This exercise strengthens the foundational algebra skills needed for solving complex equations later.

Adding and Subtracting Like Terms
Like terms are terms with the same variables and powers. These can be directly added or subtracted by combining their coefficients.

Handling Unlike Terms
Unlike terms cannot be combined. Students learn to identify and separate like and unlike terms in an expression.

Horizontal and Column Methods
The exercise introduces two formats for addition and subtraction:

• Horizontal method: Expressions are written in a single line.
• Column method: Terms are arranged one below the other to align like terms.

Use of Brackets
Students also learn how to handle brackets while adding or subtracting expressions, especially when negative signs are involved.

Simplifying Algebraic Expressions
By combining like terms and removing brackets carefully, students practice writing expressions in their simplest form.

3.0NCERT Class 8 Maths Chapter 8: Other Exercises

4.0NCERT Class 8 Maths Chapter 8 Exercise 8.2: Detailed Solutions

1. Find the product of the following pairs of monomials (i) $4,7\mathrm{p}$ (ii) $-4p,7p$ (iii) $-4\mathrm{p},7\mathrm{pq}$ (iv) $4p^3,-3p$ (v) $4\mathrm{p},0$ Sol. (i) $4\times 7\mathrm{p}=(4\times 7)\times \mathrm{p}=28\mathrm{p}$ (ii) $-4p\times 7p=(-4\times 7)\times (p\times p)$ $=-28p^{1+1}$ $=-28p^2$ (iii) $-4p\times 7pq=(-4\times 7)\times (p\times p\times q)$ $=-28p^{1+1}q$ $=-28p^{2}q$ (iv) $4p^3\times (-3p)=\{4\times (-3)\}\times \left(p^3\times p\right)$ $=-12\times p^{3+1}$ $=-12p^4$ (v) $4\mathrm{p}\times 0=(4\times 0)\times (\mathrm{p})$ $=0\times \mathrm{p}$ $=0$
2. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively : (p, q); (10m, 5n); $\left(20x^2,5y^2\right)$; (4x, $3x^2$ ); (3mn, 4np) Sol. We know that the area of a rectangle $=\ell \times \mathrm{b}$, where $\ell =$ length and $\mathrm{b}=$ breadth . Therefore, the areas of rectangles with pair of monomials (p, q); (10m, 5n); $\left(20x^2,5y^2\right)$; $\left(4x,3x^2\right)$ and ( $3\mathrm{mn},4np$ ) as their lengths and breadths are given by $p\times q=pq$ $10\mathrm{m}\times 5\mathrm{n}=(10\times 5)\times (\mathrm{m}\times \mathrm{n})=50\mathrm{mn}$ $20x^2\times 5y^2=(20\times 5)\times \left(x^2\times y^2\right)$ $=100{\mathrm{x}}^2{\mathrm{y}}^2$ $4\mathrm{x}\times 3{\mathrm{x}}^2=(4\times 3)\times \left(\mathrm{x}\times {\mathrm{x}}^2\right)$ $=12x^3$ and, $3\mathrm{mn}\times 4\mathrm{np}=(3\times 4)\times (\mathrm{m}\times \mathrm{n}\times \mathrm{n}\times \mathrm{p})$ $=12{\mathrm{mn}}^2\mathrm{p}$
3. Complete the table of products :

	2x	$-5y$	$3{\mathrm{x}}^2$	$-4xy$	$7x^{2}y$	$-9x^2{y}^2$
2x	$4{\mathrm{x}}^2$	-	-	-	-	-
-5y	-	-	$-15x^{2}y$	-	-	-
$3x^2$	-	-	-	-	-	-
$-4xy$	-	-	-	-	-	-
$7x^{2}y$	-	-	-	-	-	-
$-9x^2{y}^2$	-	-	-	-	-	-

Sol.

5.0Key Features and Benefits of Class 8 Maths Chapter 8 Exercise 8.2

• Practice in Addition and Subtraction of Algebraic Expressions: Exercise 8.2 improves the students' ability to add and subtract algebraic expressions with the help of like terms.
• Builds confidence in expression simplification: Exercise 8.2 provides an easy means to understand how to properly and step-by-step, simplify expressions.
• Strengthens basic algebra skills: Exercise 8.2 allows the student to develop their basic algebra skills, specifically addition and subtraction of polynomial expressions, so that they can appreciate and comprehend more advanced algebra topics.
• Practical applications of algebra: Understanding how expressions work allows one to solve everyday math problems faster and smarter.
• Aligned with NCERT syllabus: Each problem is exactly from the NCERT textbook, thus providing complete exam relevance and clarity.