Question

What must be added to `81x^2 - 72x + 9` to make it a perfect square?

Answer 1

A constant solution would be `7`

Another solution is `18x`

Explanation:

`81x^2-72x+9+7 = 81x^2-72x+16 = (9x-4)^2`

`81x^2-72x+9+18x = 81x^2-54x+9 = (9x-3)^2`

In general,

`(a-b)^2 = a^2-2ab+b^2`

In the above solutions, we choose to change the constant term to match the `-2ab` term or the `-2ab` term to match the `b^2` term.