Question

find the area. simplify your answer. 2x - 8 3x + 9

Explanation:

Step1: Recall area formula for triangle

The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. Here, the base is $3x + 9$ and the height is $2x-8$.

Step2: Substitute values into formula

$A=\frac{1}{2}(3x + 9)(2x - 8)$

Step3: Expand the expression

First, expand $(3x + 9)(2x - 8)$ using FOIL method:
$(3x+9)(2x - 8)=3x\times2x+3x\times(-8)+9\times2x + 9\times(-8)=6x^{2}-24x+18x-72=6x^{2}-6x - 72$.
Then, multiply by $\frac{1}{2}$: $A=\frac{1}{2}(6x^{2}-6x - 72)=3x^{2}-3x-36$.

Answer:

$3x^{2}-3x - 36$