Factor the given expression.

x2 + 16

+ 64

O A. (x+4) 2

B. (x + 16) (x + 4)

c. (x+3) (x - 8)

OD. (x+8) 2

D. (x+8) ^2

Step-by-step explanation:

x^2 + 16x + 64

We are factoring a quadratic trinomial in which the first term is x^2.

We need to find two numbers whose product is 64 and whose sum is 8.

8 * 8 = 64

8 + 8 = 16

The numbers are 8 and 8.

x^2 + 16x + 64 = (x + 8) (x + 8) = (x + 8) ^2

Check: If (x + 8) ^2 is indeed the correct factorization of x^2 + 16x + 64, then if you multiply out (x + 8) ^2, you must get x^2 + 16x + 64.

(x + 8) ^2 =

= (x + 8) (x + 8)

= x^2 + 8x + 64

= x^2 + 16x + 64

We get the correct product, so our factorization is correct.