Question

Factorize each of the following expressions:
a¹²+b¹²

Answer 1

Answer:

a×a×a×a×a×a×a×a×a×a×a×a+b×b×b×b×b×b×b×b×b×b×b×b

Answer 2

Answer:

$(a^4+b^4)(a^8-a^4b^4+b^8)$

Step-by-step explanation:

Find the suitable identity.

There is an identity $x^3+y^3=(x+y)(x^2-xy+y^2)$.

Here, $x=a^4$ and $y=b^4$.

Apply the identity.

$a^{12}+b^{12}=(a^4+b^4)(a^8-a^4b^4+b^8)$

This is irreducible factorization.

Hence the answer is ↓

$(a^4+b^4)(a^8-a^4b^4+b^8)$