Question

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

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:

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