Question

ashwin helps paint a square mural in his classroom. then he helps paint a mural in the hallway whose length is 7 feet longer and whose width is 3 feet shorter. let x represent the side length of the mural in ashwins classroom. write an expression that represents the two binomials you would multiply to find the area of the hallway mural. use that expression to find the area of the hallway mural if each side of the classroom mural is 8 feet long.
a. (x - 7)(x - 3); 5 square feet
b. (x + 7)(x + 3); 165 square feet
c. (x + 7)(x - 3); 75 square feet
d. (x - 7)(x + 3); 11 square feet

Explanation:

Step1: Determine binomials for hallway mural

The classroom mural is a square with side length \( x \). The hallway mural has length \( x + 7 \) (7 feet longer) and width \( x - 3 \) (3 feet shorter). So the binomials are \( (x + 7)(x - 3) \).

Step2: Substitute \( x = 8 \) into the expression

Substitute \( x = 8 \) into \( (x + 7)(x - 3) \):
First, calculate \( x + 7 = 8 + 7 = 15 \) and \( x - 3 = 8 - 3 = 5 \).
Then, multiply them: \( 15 \times 5 = 75 \) square feet.

Answer:

C. \((x + 7)(x - 3)\); 75 square feet