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

Question 4 Exercise 14.2

Factorise the expression:

$a^{4}+2 a^{2} b^{2}+b^{4}$

Answer:

Solution:

There are various identities, and by employing them, factorization is significantly simpler.

The provided expression to be factored has the form or can be written as: a² + 2ab + b² = (a+b)².

$\begin{aligned} & a^{4}+2 a^{2} b^{2}+b^{4} \\ =&\left(a^{2}\right)^{2}+2 \times a^{2} \times b^{2}+\left(b^{2}\right)^{2} \\ =&\left(a^{2}+\mid b^{2}\right)^{2} \\ \text {Using identity:}(x+y)^{2}=& x^{2}+2 x y+y^{2} \end{aligned}$

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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