NCERT Solutions Class 8 Mathematics Solutions for Exercise 14.2 in Chapter 14 - Factorisation

Question 25 Exercise 14.2

Factorise:

$a^{4}-2 a^{2} b^{2}+b^{4}=\left(a^{2}\right)^{2}-2 a^{2} b^{2}+\left(b^{2}\right)^{2}$

Answer:

Solution:

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Here we will be using the following two identities :

a²-2ab+b²= (a-b)² and

a²-b²= (a+b)(a-b)

$\begin{array}{l} =\left(a^{2}-b^{2}\right)^{2} \\ =((a-b)(a+b))^{2} \end{array}$

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Exercises

Exercise 14.1

Exercise 14.2

Exercise 14.3

Exercise 14.4

Chapters

Rational Numbers

Linear Equations in One Variable

Understanding Quadrilaterals

Practical Geometry

Data Handling

Squares and Square Roots

Cubes and Cube Roots

Comparing Quantities

Algebraic Expressions and Identities

Visualising Solid Shapes

Mensuration

Exponents and Powers

Direct and Inverse Proportions

Factorisation

Introduction to Graphs

Playing with Numbers