Question

{50 POINTS}

Factor completely 16x2 − 25.
(4x − 5)(4x − 5)
(4x + 5)(4x − 5)
(16x + 5)(x − 5)
(16x − 5)(x + 5)

Answer 1

`\text{Use}\ a^2-b^2=(a-b)(a+b)\\\\16x^2-25=4^2x^2-5^2=(4x)^2-5^2=(4x-5)(4x+5)\\\\Answer:\ (4x+5)(4x-5)`

Answer 2

Hello! Just by looking at the answer choices, C and D are eliminated, because those are not completely factored out. 16x² can be simplified farther than just 16x * x. With -25 being the c part, one number needs to be positive and another one needs to be negative. Plus, they have to completely cancel out, due to their being no middle part. The only answer that works in this case is B, because 4x * 4x is 16x², -5 * 4x is -20x, 5 * 4x is 20x (-20x + 20x cancel out), and 5 * -5 is 25. That simplifies to make 16x² - 25. There. The expression factored out completely is (4x + 5)(4x - 5). The answer is B.