Question

A rectangle has length: (2x + 3) and width: (x - 7). Write an expression to represent the area, and then simplify. ( A = l w)

Answer 1

To find the area of a rectangle with a length of (2x + 3) and a width of (x - 7), we multiply the two expressions and simplify the result to get an area of 2x^2 - 11x - 21 square units.

Step-by-step explanation:

To calculate the area of a rectangle, we use the formula A = lw, where A is the area, l is the length, and w is the width of the rectangle. In the given problem, the length (l) is (2x + 3) and the width (w) is (x - 7). To find an expression for the area, we multiply these two expressions:

• Area = (2x + 3)(x - 7)

To simplify, we apply the distributive property (FOIL method) to expand the expression:

• Area = 2x(x) + 2x(-7) + 3(x) + 3(-7)
• Area = 2x2 - 14x + 3x - 21
• Area = 2x2 - 11x - 21

Thus, the simplified expression for the area of the rectangle is 2x2 - 11x - 21 square units.