Answer
(11)(9)
Work Step by Step
Given the number 99 we find two numbers that are perfect squares that add to give 99. We get +100 and -1
100 - 1
*** Take the square root of 100 which is 10. Becuase 10 × 10= 100
*** Take the square root of 1 which is 1. Becuase 1 × 1= 1
We rewrite it as the squares.
$10^{2}$ - $1^{2}$
We use the formula for the difference of squares to apply to this question.
The difference of squares formula is:
$(a-b) (a+b) = a^{2} - b^{2}$
In the given formula let 12 represents a and 1 represents b.
$(10)^{2}−1^{2}$ = (10+1)(10-1)
= (10+1)(10-1)
= (11)(9)
