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

1 Answer
Dec 26, 2015

Answer:

#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#