Question

There are two distinct methods to factoring 64 - x2: Method 1: Use difference of perfect squares. Method 2: Factor out -1 and then use the difference of perfect squares. Both methods are correct. Choose one of the methods and factor the expression. In complete sentences explain why you chose the method that you did and include the final factored form of the expression in your explanation. Complete your work in the space provided.

Answer 1

`(8+x)(8-x)`

Explanation:

We need to factorize
`64-x^(2)`

We know that
`8^(2)=64`, Hence we can replace 64 and we get

`64-x^(2) =8^(2)-x^(2)`

Using
`a^(2)-b^(2)=(a+b)(a-b)` what we get is
`(8+x)(8-x)`

Hence
`64-x^(2)` can be factorized as
`(8+x)(8-x)`.

We already have an algebraic expression of this type, so using this method is time efficient.