CBSE Class 8 Maths Chapter 14: Algebraic Expressions NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 8 PDF

This chapter focuses on fundamental concepts of algebraic expressions, crucial for Class 8 Mathematics. The NCERT Solutions for Chapter 14 provide a step-by-step guide to understanding and applying these concepts. Students will learn to identify and calculate common factors of terms within algebraic expressions. Furthermore, the solutions detail the process of factorization, a key skill for simplifying and manipulating algebraic expressions. By working through these problems, students will build a strong foundation in algebra, essential for future mathematical studies. These solutions are designed to aid in exam preparation by offering clear, concise explanations and accurate methods for solving problems related to common factors and factorization.

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Board	CBSE
Class	Class 8
Subject	Mathematics
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 14

Chapter summary

Chapter 14 of the CBSE Class 8 Mathematics curriculum introduces students to algebraic expressions. This NCERT Solutions set covers exercises focused on finding common factors of terms and factorizing algebraic expressions. It breaks down complex expressions into simpler components, emphasizing the identification of shared factors. The solutions provide a clear path to understanding factorization techniques, which are vital for simplifying algebraic equations and solving more advanced problems. This chapter is foundational for building algebraic proficiency.

Learning outcomes

Understand the concept of common factors in algebraic terms.
Identify and extract common factors from given algebraic expressions.
Apply factorization techniques to simplify algebraic expressions.
Solve problems involving the factorization of binomials and polynomials.
Recognize and utilize the distributive property in reverse for factorization.

Topics covered

Paper topics

Algebraic Expressions
Terms and Factors
Common Factors
Factorization
Prime Factorization
Numerical Factors
Variable Factors
Distributive Property
Binomial Factorization
Polynomial Factorization

Important topics

Finding Common Factors
Factorizing Expressions
Identifying Numerical and Variable Factors
Using the Distributive Property for Factorization
Handling Negative Signs in Factorization

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Questions and Solutions

Exercise 14.1, Question 1

Find the common factors of the given terms:

12x, 36
2y, 22xy
14pq, 28p²q²
2x, 3x², 4
6abc, 24ab², 12a²b
16x³, -4x², 32x
10pq, 20qr, 30rp
3x²y³, 10x³y², 6x²y²z

Solution:

To find the common factors, we first find the prime factorization of each term.

The terms are 12x and 36.

Prime factorization of 12x: $12x = 2 \times 2 \times 3 \times x$

Prime factorization of 36: $36 = 2 \times 2 \times 3 \times 3$

The common factors are 2, 2, and 3. The greatest common factor is their product: $2 \times 2 \times 3 = 12$ .
The terms are 2y and 22xy.

Prime factorization of 2y: $2y = 2 \times y$

Prime factorization of 22xy: $22xy = 2 \times 11 \times x \times y$

The common factors are 2 and y. The greatest common factor is their product: $2 \times y = 2y$ .
The terms are 14pq and 28p²q².

Prime factorization of 14pq: $14pq = 2 \times 7 \times p \times q$

Prime factorization of 28p²q²: $28p^2q^2 = 2 \times 2 \times 7 \times p \times p \times q \times q$

The common factors are 2, 7, p, and q. The greatest common factor is their product: $2 \times 7 \times p \times q = 14pq$ .
The terms are 2x, 3x², and 4.

Prime factorization of 2x: $2x = 2 \times x \times 1$

Prime factorization of 3x²: $3x^2 = 3 \times x \times x \times 1$

Prime factorization of 4: $4 = 2 \times 2 \times 1$

The only common factor among all three terms is 1.
The terms are 6abc, 24ab², and 12a²b.

Prime factorization of 6abc: $6abc = 2 \times 3 \times a \times b \times c$

Prime factorization of 24ab²: $24ab^2 = 2 \times 2 \times 2 \times 3 \times a \times b \times b$

Prime factorization of 12a²b: $12a^2b = 2 \times 2 \times 3 \times a \times a \times b$

The common factors are 2, 3, a, and b. The greatest common factor is their product: $2 \times 3 \times a \times b = 6ab$ .
The terms are 16x³, -4x², and 32x.

Prime factorization of 16x³: $16x^3 = 2 \times 2 \times 2 \times 2 \times x \times x \times x$

Prime factorization of -4x²: $-4x^2 = (-1) \times 2 \times 2 \times x \times x$

Prime factorization of 32x: $32x = 2 \times 2 \times 2 \times 2 \times 2 \times x$

The common numerical factors are 2 and 2. The common variable factor is x. The greatest common factor is their product: $2 \times 2 \times x = 4x$ .
The terms are 10pq, 20qr, and 30rp.

Prime factorization of 10pq: $10pq = 2 \times 5 \times p \times q$

Prime factorization of 20qr: $20qr = 2 \times 2 \times 5 \times q \times r$

Prime factorization of 30rp: $30rp = 2 \times 3 \times 5 \times r \times p$

The common factors are 2 and 5. The greatest common factor is their product: $2 \times 5 = 10$ .
The terms are 3x²y³, 10x³y², and 6x²y²z.

Prime factorization of 3x²y³: $3x^2y^3 = 3 \times x \times x \times y \times y \times y$

Prime factorization of 10x³y²: $10x^3y^2 = 2 \times 5 \times x \times x \times x \times y \times y$

Prime factorization of 6x²y²z: $6x^2y^2z = 2 \times 3 \times x \times x \times y \times y \times z$

The common variable factors are x² and y². The greatest common factor is their product: $x \times x \times y \times y = x^2 y^2$ .

Exercise 14.1, Question 2

Factorize the following expressions:

7x - 42
6p - 12q
7a² + 14a
-16z + 20z³
20l²m + 30alm
5x²y - 15xy²
10a² - 15b² + 20c²
-4a² + 4ab - 4ca
x²yz + xy²z + xyz²
ax²y + bxy² + cxyz

Solution:

To factorize these expressions, we identify the greatest common factor (GCF) of the terms and use the distributive property in reverse.

The expression is $7x - 42$ .

The terms are $7x$ and $-42$ .

Prime factorization of $7x = 7 \times x$ .

Prime factorization of $42 = 2 \times 3 \math>7$ .

The greatest common factor is 7.

Factoring out 7: $7(x - 6)$ .
The expression is $6p - 12q$ .

The terms are $6p$ and $-12q$ .

Prime factorization of $6p = 2 \times 3 \times p$ .

Prime factorization of $12q = 2 \times 2 \times 3 \times q$ .

The greatest common factor is $2 \times 3 = 6$ .

Factoring out 6: $6(p - 2q)$ .
The expression is $7a^2 + 14a$ .

The terms are $7a^2$ and $14a$ .

Prime factorization of $7a^2 = 7 \times a \times a$ .

Prime factorization of $14a = 2 \times 7 \times a$ .

The greatest common factor is $7 \times a = 7a$ .

Factoring out 7a: $7a(a + 2)$ .
The expression is $-16z + 20z^3$ .

The terms are $-16z$ and $20z^3$ .

Prime factorization of $16z = 2 \times 2 \math>2 \times 2 \times z$ .

Prime factorization of $20z^3 = 2 \times 2 \times 5 \times z \times z \times z$ .

The greatest common factor of the coefficients 16 and 20 is 4. The greatest common factor of the variables z and z³ is z. So, the GCF is $4z$ . We can also factor out $-4z$ to make the first term positive.

Factoring out $-4z$ : $-4z(4 - 5z^2)$ .
The expression is $20l^2m + 30alm$ .

The terms are $20l^2m$ and $30alm$ .

Prime factorization of $20l^2m = 2 \times 2 \times 5 \times l \times l \times m$ .

Prime factorization of $30alm = 2 \times 3 \math>5 \times a \times l \times m$ .

The greatest common factor is $2 \times 5 \times l \times m = 10lm$ .

Factoring out 10lm: $10lm(2l + 3a)$ .
The expression is $5x^2y - 15xy^2$ .

The terms are $5x^2y$ and $-15xy^2$ .

Prime factorization of $5x^2y = 5 \times x \times x \times y$ .

Prime factorization of $15xy^2 = 3 \times 5 \times x \times y \times y$ .

The greatest common factor is $5 \times x \times y = 5xy$ .

Factoring out 5xy: $5xy(x - 3y)$ .
The expression is $10a^2 - 15b^2 + 20c^2$ .

The terms are $10a^2$ , $-15b^2$ , and $20c^2$ .

Prime factorization of $10a^2 = 2 \times 5 \times a \times a$ .

Prime factorization of $15b^2 = 3 \times 5 \times b \times b$ .

Prime factorization of $20c^2 = 2 \times 2 \times 5 \times c \times c$ .

The greatest common factor among the coefficients is 5. There are no common variable factors across all terms.

Factoring out 5: $5(2a^2 - 3b^2 + 4c^2)$ .
The expression is $-4a^2 + 4ab - 4ca$ .

The terms are $-4a^2$ , $4ab$ , and $-4ca$ .

Prime factorization of $4a^2 = 2 \times 2 \times a \times a$ .

Prime factorization of $4ab = 2 \times 2 \times a \times b$ .

Prime factorization of $4ca = 2 \times 2 \times c \times a$ .

The greatest common factor is $2 \times 2 \times a = 4a$ . We can factor out $-4a$ to make the first term positive.

Factoring out $-4a$ : $-4a(a - b + c)$ .
The expression is $x^2yz + xy^2z + xyz^2$ .

The terms are $x^2yz$ , $xy^2z$ , and $xyz^2$ .

Prime factorization of $x^2yz = x \times x \times y \times z$ .

Prime factorization of $xy^2z = x \times y \times y \times z$ .

Prime factorization of $xyz^2 = x \times y \times z \times z$ .

The greatest common factor is $x \times y \times z = xyz$ .

Factoring out xyz: $xyz(x + y + z)$ .
The expression is $ax^2y + bxy^2 + cxyz$ .

The terms are $ax^2y$ , $bxy^2$ , and $cxyz$ .

Prime factorization of $ax^2y = a \times x \times x \times y$ .

Prime factorization of $bxy^2 = b \times x \times y \times y$ .

Prime factorization of $cxyz = c \times x \times y \times z$ .

The greatest common factor is $x \times y = xy$ .

Factoring out xy: $xy(ax + by + cz)$ .

Common mistakes

Incorrectly identifying all common factors, especially numerical coefficients.
Errors in handling negative signs during factorization.
Missing common factors when dealing with multiple terms or variables.
Confusing factorization with expansion.
Mistakes in applying the distributive property in reverse.

Revision tips

Practice identifying common numerical and variable factors systematically.
Review the prime factorization of coefficients to ensure all common factors are found.
Work through each factorization example, paying attention to the signs.
Try to factorize expressions in multiple ways to deepen understanding.
Use the solutions to check your work and understand alternative approaches.

Practice MCQs

Q1. What is the greatest common factor of 12x and 36?

Q2. Which of the following is a factor of 7 $a^2$ + 14a?

Q3. Factorizing 6p - 12q results in:

Q4. What is the common factor in the expression 5 $x^2$ y - 15x $y^2$ ?

Q5. Factorizing -16z + 20 $z^3$ involves finding common factors of:

Frequently asked questions

What is the main focus of CBSE Class 8 Maths Chapter 14?

Chapter 14 of CBSE Class 8 Maths focuses on algebraic expressions, specifically on finding common factors of terms and factorizing these expressions.

How do these NCERT Solutions help in understanding factorization?

The solutions provide detailed, step-by-step explanations for each problem, breaking down the process of identifying common factors and applying factorization techniques, making it easier for students to grasp the concepts.

What are common factors in algebraic expressions?

Common factors are the factors (numerical or variable) that are present in all the terms of an algebraic expression. For example, in 12x and 36, the common factors are 2, 2, and 3, leading to a greatest common factor of 12.

Why is factorization important in algebra?

Factorization is important because it simplifies algebraic expressions, helps in solving equations, and is a fundamental skill for understanding more advanced algebraic concepts.

Are the questions in the NCERT Solutions the same as in the textbook?

Yes, the questions in these NCERT Solutions are identical to those in the textbook, ensuring that students are practicing the exact problems prescribed by the board.

How are the solutions presented?

Each solution is rewritten to be clearer and more comprehensive, showing the step-by-step process, including prime factorization where applicable, and highlighting the final factored form of the expression.

Content reviewed by the NCERT Help team. Editorial Team and update policy

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