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

Answer:

Step-by-step 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;

$Bags = \frac{x^2+18x+81}{x^2 - 81}$

Expand the numerator

$Bags = \frac{x^2+9x+9x+81}{x^2 - 81}$

$Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}$

$Bags = \frac{(x+9)(x+9)}{x^2 - 81}$

Express 81 as 9²

$Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}$

Evaluate as difference of two squares

$Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}$

$Bags = \frac{(x+9)}{(x - 9)}$

Hence, the number of bags is $Bags = \frac{(x+9)}{(x - 9)}$