Factor (y+2)^2-81
difference of squares ...
( (y+2) + 9)( (y+2) - 9)
= (y+11)(y-7)
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To factor the expression (y+2)^2 - 81, we can use a difference of squares formula.
Step 1: Recognize the Difference of Squares Formula
The difference of squares formula states that for any two numbers a and b, the expression a^2 - b^2 can be factored as (a + b)(a - b).
Step 2: Identify the Values for 'a' and 'b'
In our expression (y+2)^2 - 81, we have (y+2)^2 as a^2 and 81 as b^2. Therefore, 'a' is equal to (y+2) and 'b' is equal to 9 (since 9^2 = 81).
Step 3: Apply the Difference of Squares Formula
Using the formula from Step 1, we can factor the expression as follows:
((y+2)+9)((y+2)-9)
Step 4: Simplify the Factors
Simplifying the factors, we get:
(y + 2 + 9)(y + 2 - 9)
which further simplifies to:
(y + 11)(y - 7)
So, the expression (y+2)^2 - 81 can be factored as (y + 11)(y - 7).