Question

what is (16x^2 - 25) factored completely?
a ((4x + 5)(4x - 5))
b ((4x - 5)^2)
c ((-4x + 5)(4x - 5))
d ((4x + 5)^2)

Explanation:

Step1: Identify the form

The expression \(16x^2 - 25\) is a difference of squares, which has the form \(a^2 - b^2\), where \(a = 4x\) (since \((4x)^2=16x^2\)) and \(b = 5\) (since \(5^2 = 25\)).

Step2: Apply difference of squares formula

The formula for factoring a difference of squares is \(a^2 - b^2=(a + b)(a - b)\). Substituting \(a = 4x\) and \(b = 5\) into the formula, we get \((4x + 5)(4x - 5)\).

Answer:

A. \((4x + 5)(4x - 5)\)