Question

Please help and show me how you got it as best as possible step by step im struggling and need to show my work

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for area of a rectangle

$Area=length\times width$

STEP 2: Write the given measure of the sides

$\begin{gathered} length=3x+2 \\ width=2x-1 \end{gathered}$

STEP 3: Calculate the area

By substitution,

$\begin{gathered} Area=(3x+2)(2x-1) \\ \mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd \\ \left(3x+2\right)\left(2x-1\right)=3x\cdot \:2x+3x\left(-1\right)+2\cdot \:2x+2\left(-1\right) \\ =3x\cdot \:2x+3x\left(-1\right)+2\cdot \:2x+2\left(-1\right) \\ =6x^2+x-2 \end{gathered}$

Hence, the area of the rectangle is

$6x^2+x-2$