Answer:
[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]
Step-by-step explanation:
The given expression is
[tex]a^{4}-b^{4}[/tex]
This expression is the difference of two perfect squares, and their square roots are
[tex]\sqrt{a^{4}} =a^{2}\\ \sqrt{b^{4}} =b^{2}[/tex]
Now, the difference of two perfect squares can be factored as
[tex]x^{2} -y^{2}=(x+y)(x-y)[/tex]
So, if we apply this rule, the result would be
[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]
Therefore, the simplest form of the binomial expression is
[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]
