Question

factorise a⁸-2a⁴b⁴+b⁸​

Answer 1

a⁸-2a⁴b⁴+b⁸​

as per equation  it is same as (a-b)²

hence change as

(a⁴ - b⁴)²

 

a⁸-2a⁴b⁴+b⁸​

=  (a⁴ - b⁴)²

Answer 2

Given equation is,

$a^{8} -2a^{4} b^{4}+b^{8}$

Now we have to factorize the given equation $a^{8} -2a^{4} b^{4}+b^{8}$

Also this equation can be written as,

$(a^{4}) ^{2} -2a^{4} b^{4} +(b^{4}) ^{2}$

The above equation is in the form of $a^{2}-2ab+b^{2}$

The formula can be written as,

Formula:

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

Here,

$a=a^{4}$

$b=b^{4}$

Substitute these values in the formula.

We get,

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

Therefore, the final answer after factorization is $(a^{4}-b^{4} ) ^{2}$.