Answer:
The expression for the shaded region is 10x² + 12x .
Step-by-step explanation:
First, you have to find the area of both rectangles using the formula :
[tex]area = length \times height[/tex]
Small rectangle,
[tex]area = x \times (5x - 2)[/tex]
[tex]area = 5 {x}^{2} - 2x[/tex]
Large rectangle,
[tex]area = (3x + 2) \times 5x[/tex]
[tex]area = 15 {x}^{2} + 10x[/tex]
In order to find the shaded region, you have to subtract the smaller from the larger one :
[tex]area \: of \: shaded = large - small[/tex]
[tex]area = 15 {x}^{2} + 10x - 5 {x}^{2} + 2x [/tex]
[tex]area = 10 {x}^{2} + 12x[/tex]
