Final answer:
The expression v²+10v+25-x² factors as (v+5+x)(v+5-x), by recognizing that v²+10v+25 is a perfect square trinomial and the entire expression is a difference of squares.
Step-by-step explanation:
The student is asking how to factor the algebraic expression v²+10v+25-x². To approach this problem, we need to recognize that v²+10v+25 is a perfect square trinomial, which factors into (v+5)². The expression x² can be written as (x)². The given expression is a difference of squares and can be factored as (v+5+x)(v+5-x). This technique is fundamental in algebra and is used to simplify expressions and solve equations.