Factor. $$ 81-(p-5)^{2} $$ $$ 81-(p-5)^{2}=\square $$ (Simplify your answer. Type your answer in factored form.

Question

UpStudy AI · Accepted Answer

We start with the expression:

81 – (p – 5)²

Notice that 81 is the same as 9², so the expression is a difference of two squares:

9² – (p – 5)²

The difference of squares formula tells us that:

a² – b² = (a – b)(a + b)

Here, a = 9 and b = (p – 5). Applying the formula:

81 – (p – 5)² = (9 – (p – 5)) · (9 + (p – 5))

Now, simplify each factor:

1. The first factor:
  9 – (p – 5) = 9 – p + 5 = 14 – p

2. The second factor:
  9 + (p – 5) = 9 + p – 5 = p + 4

Thus, the fully factored form is:

(14 – p)(p + 4)

So, the final answer is:

81 – (p – 5)² = (14 – p)(p + 4)
$$ 81 - (p - 5)^2 = (14 - p)(p + 4) $$

Factor. \( 81-(p-5)^{2} \) \( 81-(p-5)^{2}=\square \) (Simplify your answer. Type your answer in factored form.