Question

1. compute the following products. (hint: draw an area model)

a. $(4x + 5)(4x - 5)$
b. $(4x + 5)^2$

Explanation:

Step1: Apply difference of squares rule

For $(a+b)(a-b)=a^2-b^2$, let $a=4x$, $b=5$.

$$\begin{align*} (4x+5)(4x-5)&=(4x)^2 - 5^2\\ &=16x^2 - 25 \end{align*}$$

Step2: Expand the squared binomial

For $(a+b)^2=a^2+2ab+b^2$, let $a=4x$, $b=5$.

$$\begin{align*} (4x+5)^2&=(4x)^2 + 2(4x)(5) + 5^2\\ &=16x^2 + 40x + 25 \end{align*}$$

Answer:

a. $16x^2 - 25$
b. $16x^2 + 40x + 25$