Question

Simplify:
(3x + 2y)(4x + 3y) − (2x − y)(7x − 3y)

Answer 1

To simplify, we will proceed as follows:

$$\begin{gathered} \left(3x+2y\right)\left(4x+3y\right)-\left(2x-y\right)\left(7x-3y\right) \\ =\left[\left(3x+2y\right)\left(4x+3y\right)\right]-\left[\left(2x-y\right)\left(7x-3y\right)\right] \end{gathered}$$
$=\left[3x\left(4x+3y\right)+2y\left(4x+3y\right)\right]-\left[2x\left(7x-3y\right)-y\left(7x-3y\right)\right]$ (Distributive law)
$$\begin{gathered} =12x^2+9xy+8xy+6y^2-\left[14x^2-6xy-7xy+3y^2\right] \\ =12x^2+9xy+8xy+6y^2-14x^2+6xy+7xy-3y^2 \end{gathered}$$
$=12x^2-14x^2+9xy+8xy+6xy+7xy+6y^2-3y^2$ (Rearranging)
$=-2x^2+30xy+3y^2$ (Combining like terms)

Thus, the answer is $-2x^2+30xy+3y^2$.