the dimensions of a sand volleyball court are represented by a width of (6y - 5) ft and a length of (3y +…

the dimensions of a sand volleyball court are represented by a width of (6y - 5) ft and a length of (3y + 4). write a simplified expression representing the area of the court. enter your response in the space provided below.

the dimensions of a sand volleyball court are represented by a width of (6y - 5) ft and a length of (3y + 4). write a simplified expression representing the area of the court. enter your response in the space provided below.

Answer

Explanation:

Step1: Recall area formula

The area $A$ of a rectangle is $A = \text{length}\times\text{width}$. Here, length $l=3y + 4$ and width $w = 6y-5$. So $A=(3y + 4)(6y - 5)$.

Step2: Expand using FOIL method

$(3y+4)(6y - 5)=3y\times6y+3y\times(- 5)+4\times6y + 4\times(-5)$.

Step3: Calculate each term

$3y\times6y=18y^{2}$, $3y\times(-5)=-15y$, $4\times6y = 24y$, $4\times(-5)=-20$.

Step4: Combine like - terms

$18y^{2}-15y + 24y-20=18y^{2}+(-15 + 24)y-20=18y^{2}+9y-20$.

Answer:

$18y^{2}+9y - 20$