Question

1. draw generic rectangles to match each calculation, and use your rectangles to find the area.

a. (2x - 3y)(3x - 2y)=
b. (x - y - 10)(y - x)=

Explanation:

Step1: Expand (2x - 3y)(3x - 2y) using FOIL method

\[

$$\begin{align*} &(2x-3y)(3x - 2y)\\ =&2x\times3x+2x\times(- 2y)+(-3y)\times3x+(-3y)\times(-2y)\\ =&6x^{2}-4xy - 9xy+6y^{2}\\ =&6x^{2}-13xy + 6y^{2} \end{align*}$$

\]

Step2: Expand (x - y - 10)(y - x)

\[

$$\begin{align*} &(x - y - 10)(y - x)\\ =&x(y - x)-y(y - x)-10(y - x)\\ =&xy-x^{2}-y^{2}+xy-10y + 10x\\ =&-x^{2}-y^{2}+2xy+10x-10y \end{align*}$$

\]

Answer:

a. $6x^{2}-13xy + 6y^{2}$
b. $-x^{2}-y^{2}+2xy+10x-10y$