Question

a. write an expression for the area of the shaded region.
b. write the expression in factored form.
a. the area of the shaded region is
(do not factor.)

Explanation:

Step1: Find area of large square

The side - length of the large square is $x$, so its area $A_{1}=x^{2}$ (using the formula for the area of a square $A = s^{2}$, where $s$ is the side - length).

Step2: Find area of small square

The side - length of the small square is 4, so its area $A_{2}=4^{2}=16$.

Step3: Calculate area of shaded region

The area of the shaded region $A$ is the area of the large square minus the area of the small square. So $A=x^{2}-16$.

Step4: Factor the expression

We use the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$. Here $a = x$ and $b = 4$, so $x^{2}-16=(x + 4)(x - 4)$.

Answer:

a. $x^{2}-16$
b. $(x + 4)(x - 4)$