Answer:
[tex]100-p^{16}=(10-p^{8})(10+p^{8})[/tex]
Step-by-step explanation:
Factoring
Binomial factoring is a common task when solving a great variety of math problems.
One of the best-known formula that helps us to factor a binomial is:
[tex](a^2-b^2)=(a-b)(a+b)[/tex]
It can easily be identified because the expression is the difference between two perfect squares.
The expression
[tex]100-p^{16}[/tex]
can be factored with the formula above since it's the difference of two squares:
[tex]a=\sqrt{100}=10[/tex]
[tex]b=\sqrt{p^{16}}=p^{8}[/tex]
The expression is factored as follows:
[tex]\boxed{100-p^{16}=(10-p^{8})(10+p^{8})}[/tex]
