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}



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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