Question

Which expression is equivalent to x2 - 8x + 16? A. (x+4)2 B. (x-4)2 C. (x-4)(x+4) D. (x-8)(x+2)

Answer 1

B.
`(x - 4)^2`

Explanation:

To determine the equivalent expression of
`x^2 - 8x + 16`, factorise the given expression as follows:

`x^2 - 8x + 16`

Look for two numbers that will give you "-8" when added together, and will equally give you "16" when multiplied together.

Thus: -4 + -4 = -8; also, -4 × -4 = 16.

Therefore, -4x and -4x is what we would use to replace "-8x" in the expression as follows:

`x^2 - 4x - 4x + 16`

`x(x - 4) -4(x - 4)`

`(x - 4)(x - 4)`

`(x - 4)(x - 4) = (x - 4)^2`

Therefore,
`x^2 - 8x + 16 = (x - 4)^2`