Question

Write a polynomial in two variables that describe the total area of the shaded region. Distribute and simplify your answer.

Answer 1

The length and width of the rectangle is l = 8x +3y and w = 6x + 9y.

The formula for the area of rectangle is,

$A=l\cdot w$

Determine the expression for the area of rectangle.

$\begin{gathered} A=(6x+9y)\cdot(8x+3y) \\ =6x\cdot8x+6x\cdot3y+9y\cdot8x+9y\cdot3y \\ =48x^2+18xy+72xy+27y^2 \\ =48x^2+90xy+27y^2 \end{gathered}$

Thus answer is,

$48x^2+90xy+27y^2$