Question

write a simplified polynomial expression in standard form to represent the area of the rectangle below. x - 4 5x + 2 5x^2 + 18x - 2 5x^2 + 13x + 2 5x^2 - 18x - 8 5x^2 + 13x + 8

Explanation:

Step1: Recall area formula

The area $A$ of a rectangle is $A = \text{length}\times\text{width}$. Here, length $l=5x + 2$ and width $w=x - 4$. So $A=(5x + 2)(x - 4)$.

Step2: Use FOIL method

$(5x + 2)(x - 4)=5x\times x+5x\times(-4)+2\times x+2\times(-4)$.

Step3: Simplify each term

$5x\times x = 5x^{2}$, $5x\times(-4)=-20x$, $2\times x = 2x$, $2\times(-4)=-8$.

Step4: Combine like - terms

$5x^{2}-20x + 2x-8=5x^{2}+(-20x + 2x)-8=5x^{2}-18x - 8$.

Answer:

$5x^{2}-18x - 8$