Question

How do you factor `y= 4x^2 – 36x+ 81` ?

Answer 1

`4x^2-36x+81 = (2x-9)^2`

Explanation:

We can recognise this as a perfect square trinomial.

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

In our example notice that `4x^2 = (2x)^2` and `81=9^2` are both perfect squares, so the question is, if we let `a=2x` and `b=9` then does `+-2ab` match the middle term `-36x`. Yes with a minus sign.

Hence:

`4x^2-36x+81 = (2x-9)^2`