Question

geometry concepts/connect a - 27.0821010 - 812 - king, tyrone ga - 3: mathxl king_walley find the area of the rectangle. (2x + 5) yards (2x - 5) yards the area of the rectangle is (simplify your answer.)

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l=(2x + 5)$ and $w=(2x - 5)$.

Step2: Apply FOIL method

$(2x + 5)(2x - 5)=2x\times2x+2x\times(- 5)+5\times2x + 5\times(-5)$.

Step3: Simplify terms

$2x\times2x=4x^{2}$, $2x\times(-5)=-10x$, $5\times2x = 10x$, $5\times(-5)=-25$. Then $4x^{2}-10x + 10x-25$.

Step4: Combine like - terms

$-10x$ and $10x$ cancel out, so the result is $4x^{2}-25$.

Answer:

$4x^{2}-25$