Question

What is the simplest form of this binomial expression? a4 − b4

Answer 1

Answer:

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

Step-by-step explanation:

The given expression is

$a^{4}-b^{4}$

This expression is the difference of two perfect squares, and their square roots are

$\sqrt{a^{4}} =a^{2}\\ \sqrt{b^{4}} =b^{2}$

Now, the difference of two perfect squares can be factored as

$x^{2} -y^{2}=(x+y)(x-y)$

So, if we apply this rule, the result would be

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

Therefore, the simplest form of the binomial expression is

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