Question

factor $16p^2 - 25$:
a. $(-4p + 5)(4p - 5)$
b. $(4p + 5)(4p - 5)$
c. $(4p - 5)^2$
d. $(p + 4)(p - 4)$

Explanation:

Step1: Recognize difference of squares

The expression $16p^2 - 25$ is a difference of perfect squares, since $16p^2=(4p)^2$ and $25=5^2$.

Step2: Apply difference of squares formula

Use the identity $a^2 - b^2=(a+b)(a-b)$, where $a=4p$ and $b=5$.
$$16p^2 - 25=(4p)^2 - 5^2=(4p+5)(4p-5)$$

Answer:

b. $(4p + 5)(4p - 5)$