Question

find the area of the shaded region.
the area of the shaded region is
(simplify your answer. do not factor.)

Explanation:

Step1: Find area of large square

The side - length of the large square is $(5x - 2)$ meters. The area of a square is $A = s^2$, so the area of the large square $A_{1}=(5x - 2)^2=(5x - 2)(5x - 2)=25x^{2}-20x + 4$ square meters.

Step2: Find area of small square

The side - length of the small square is $(x + 1)$ meters. The area of a square is $A = s^2$, so the area of the small square $A_{2}=(x + 1)^2=(x + 1)(x + 1)=x^{2}+2x + 1$ square meters.

Step3: Find area of shaded region

The area of the shaded region $A=A_{1}-A_{2}$. Substitute the expressions for $A_{1}$ and $A_{2}$: $A=(25x^{2}-20x + 4)-(x^{2}+2x + 1)=25x^{2}-20x + 4 - x^{2}-2x - 1=24x^{2}-22x + 3$ square meters.

Answer:

$24x^{2}-22x + 3$ square meters