Question

The dimensions of a playground are represented by a width of 9x + 1 feet and a length of 5x – 2 feet. Write a simplified expression that represents the area of the playground. Write your answer in standard form.

Answer 1

The simplified expression that represents the area of the playground with dimensions 9x + 1 feet in width and 5x – 2 feet in length, in standard form, is A = 45x^2 - 13x - 2.

Step-by-step explanation:

To find the area of the playground, you will need to multiply the width by the length. The width is given as 9x + 1 feet, and the length is 5x – 2 feet. Multiplying the two expressions together, the area A can be expressed as:

A = (9x + 1)(5x – 2)

First, we use the distributive property (also known as the FOIL method for binomials) to multiply these two expressions:

A = (9x × 5x) + (9x × (–2)) + (1 × 5x) + (1 × (–2))

A = 45x^2 - 18x + 5x - 2

Now, combine like terms:

A = 45x^2 - 13x - 2

This expression represents the area of the playground in standard form.