Given:
Area of large rectangle = (8x + 1)(5x)
Area of small rectangle = (4x)(2x)
To find area of the shaded region, subtract the area of the small rectangle from the large rectangle.
We have:
Area of large rectangle =
[tex]\begin{gathered} (8x+1)(5x) \\ \\ =8x(5x)+1(5x) \\ \\ =40x^2+5x \end{gathered}[/tex]
Area of small rectangle =
[tex]\begin{gathered} (4x)(2x) \\ \\ =8x^2 \end{gathered}[/tex]
Area of shaded region =
[tex]\begin{gathered} (40x^2+5x)-(8x^2) \\ \\ 40x^2+5x-8x^2 \\ \\ \text{Combine like terms:} \\ 40x^2-8x^2+5x \\ \\ =32x^2+5x \end{gathered}[/tex]
Therefore, the area of the shaded region is = 32x² + 5x
ANSWER:
[tex]32x^{2}+5x[/tex]
