Question

X^2 - 25factor each expression completely

Answer 1

For the development of the exercise, we will need to remember some aspects of the factorization cases, specifically, the difference of squares. The first thing to do is to check if our algebraic expression complies with the rules to be able to apply this factorization case:

-Be a binomial

-Be separated by a minus sign.

-Each term must have an exact square root.

As it meets these criteria, we proceed to apply the factorization case as follows

$\begin{gathered} (x-5)(x+5) \\ \text{ To prove the result:} \\ (x-5)(x+5)=x^2+5x-5x-25=x^2-25 \end{gathered}$

Thus, the factorization for this expression is x^2-25= (x-5)(x+5).