Question

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Question 2 Part C (5 points): Mrs. Hinson is replacing her rectangular driveway with pavers. The area of her driveway is 64m² - 9n² square units. Mrs. Hinson needs to find the dimensions of her driveway so she knows how many pavers to buy.


Help Mrs. Hinson by factoring the area completely. To receive full credit, you must show all work.


WORK:
ANSWER: The dimensions are...

Answer 1

Let's factor out

$\\ \rm\Rrightarrow 64m^2-9n^2$

$\\ \rm\Rrightarrow (8m)^2-(3n)^2$

$\\ \rm\Rrightarrow (8m-3n)(8m+3n)$

Done

Answer 2

The dimensions of Mrs. Hinson's driveway are (8m -3n)unit ×  (8m + 3n) units.

Factors:

• It is a number or algebraic expression which divides completely another number or expression, without leaving any remainder.

How to solve the given problem?

• The shape of the driveway is rectangular, which is given by
  64m² - 9n² .
• Let A = 64m² - 9n².
  ∴ Splitting the given quadratic equation as it is in form of
     a² - b² = (a - b) (a + b)
  ∴ A = (8m)² - (3n)²
  ∴ A = (8m -3n) (8m + 3n)   [∵a² - b² = (a - b) (a + b)]
• Thus the factors of the equation are  (8m -3n) (8m + 3n).
  

Thus, the dimensions of the area are  (8m -3n)unit ×  (8m + 3n) units.

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