Question

Which number should be added to the expression x^2-8x to change it into a perfect square trinomial?

a. -16
b. -4
c. 4
d. 16

Answer 1

The perfect square
`(x-a)^2` can be expanded as follows:

`(x-a)^2=x^2-2ax+a^2`

So, we have to think of the term
`-8x` as
`-2ax`, which implies
`a=4`.

Thus, we have to add
`a^2`, i.e. 16, to complete the perfect square:

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