The Options are:
- (A)(5x+y)(x-8y)
- (B) (5x+8y)(5x-8y)
- (C)(5x+8y)(5x+8y)
- (D) (5x-8y)(5x-8y)
Answer:
(B) (5x-8y)(5x+8y)
Step-by-step explanation:
Given the binomial: [tex]25x^2-64y^2[/tex]
[tex]25x^2-64y^2\\=5^2x^2-8^2y^2\\=(5x)^2-(8y)^2[/tex]
The essence of expressing it in this form is so as to be able to apply a principle of factorization called the "Difference of Two Squares"
Difference of Two Squares: [tex]a^2-b^2=(a-b)(a+b)[/tex]
Therefore taking: a=5x; b=8y
[tex](5x)^2-(8y)^2=(5x-8y)(5x+8y)\\[/tex]
Thus (5x-8y)(5x+8y) is the factorization of the binomial [tex]25x^2-64y^2[/tex].
The correct option is B
