Question

Factorise : a 4 + 2a 2 b 2 + b 4

Answer 1

(a2)2+2a2b2+(b2)2
this is in the form of( a+b)2=a2+2ab+b2
therefore a4+2a2b2+b4=(a2+b2)
hope it helps pls mark it as brainliest

Answer 2

The factorisation of $a^{4} +2a^{2} b^{2} +b^{4}$ is $(a^{2} +b^{2})(a^{2} +b^{2}).$

Step-by-step explanation:

We have,

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

To find, the factorisation of $a^{4} +2a^{2} b^{2} +b^{4}$ = ?

∴ $a^{4} +2a^{2} b^{2} +b^{4}$

= $(a^{2})^{2} +2(a^{2}) (b^{2}) +(b^{2})^{2}$

Put $A=a^{2}  and B=b^{2}$

∴ $A^{2} +2AB +B^{2}$

= $(A+B)^{2} =(A+B)(A+B)$    ....(1)

[Using identity, $(A+B)^{2} =(A+B)(A+B)$]

Put$A=a^{2}$ and $B=b^{2}$, we get

∴ $a^{4} +2a^{2} b^{2} +b^{4}=(a^{2} +b^{2})(a^{2} +b^{2})$

Hence, the factorisation of $a^{4} +2a^{2} b^{2} +b^{4}$ is $(a^{2} +b^{2})(a^{2} +b^{2}).$