Question

Find the expression that is equivalent to:

x2 - 16x + 64

a (x – 8)(x + 8)
b (x + 8)(x + 8)
c (x + 8)^2
d (x – 8)^2

Answer 1

D. (x – 8)^2

Explanation:

x2 - 16x + 64:

Step 1: Use the sum-product pattern.

`x^(2) -16x+64\\x^(2) -8x-8x+64`

Step 2: Common factor from the two pairs.

`x^(2) -8x-8x+64\\x(x-8)-8(x-8)`

Step 3: Rewrite in factored form.

`x(x-8)-8(x-8)\\(x-8)(x-8)`

Step 4: Combine to a square.

`(x-8)(x-8)\\(x-8)^(2)`