Question

find the product.
(5q + 4) - p(5q + 4) + p
(5q + 4) - p(5q + 4) + p = \square

Explanation:

Step1: Recognize difference of squares

The expression matches $(a-b)(a+b)=a^2-b^2$, where $a=5q+4$, $b=p$.

Step2: Expand $a^2$

$$(5q+4)^2=(5q)^2+2(5q)(4)+4^2=25q^2+40q+16$$

Step3: Compute $a^2-b^2$

Substitute $a^2$ and $b^2=p^2$:
$$25q^2+40q+16-p^2$$

Answer:

$25q^2 + 40q + 16 - p^2$