2712.sagews

Firstly remember that

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

so if you're given a term like

y^2 + 8y

you can complete the square by thinking of it as the

x^2 + 2ax

part of the right hand term above. with a as 4. now that we have a we can write

(y + 4)^2 = y^2 + 8y + 8^2

but since we want

y^2 + 8y

we subtract

8^2

from both sides giving

(y+4)^2 - 64 = y^2 + 8y

and the left hand side is the completed square representation we were looking for.