Question

Which shows the factored form of the expression below? 100-p^16 (show all steps you took to get to answer)

Answer 1

Answer:

$100-p^{16}=(10-p^{8})(10+p^{8})$

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:

$(a^2-b^2)=(a-b)(a+b)$

It can easily be identified because the expression is the difference between two perfect squares.

The expression

$100-p^{16}$

can be factored with the formula above since it's the difference of two squares:

$a=\sqrt{100}=10$

$b=\sqrt{p^{16}}=p^{8}$

The expression is factored as follows:

$\boxed{100-p^{16}=(10-p^{8})(10+p^{8})}$