Question

Aaron wants to mulch his garden. His garden is x^2+18x+81 ft^2 One bag of mulch covers x^2-81 ft^2 . Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.

Answer 1

Explanation:

Given

Garden:
`x^2+18x+81`

One Bag:
`x^2 - 81`

Requires

Determine the number of bags to cover the whole garden

This is calculated as thus;

`Bags = (x^2+18x+81)/(x^2 - 81)`

Expand the numerator

`Bags = (x^2+9x+9x+81)/(x^2 - 81)`

`Bags = (x(x+9)+9(x+9))/(x^2 - 81)`

`Bags = ((x+9)(x+9))/(x^2 - 81)`

Express 81 as 9²

`Bags = ((x+9)(x+9))/(x^2 - 9\²)`

Evaluate as difference of two squares

`Bags = ((x+9)(x+9))/((x - 9)(x+9))`

`Bags = ((x+9))/((x - 9))`

Hence, the number of bags is
`Bags = ((x+9))/((x - 9))`