How do you factor x^3-18x^2+81x?

1 Answer
Jun 14, 2015

Separate the common x factor then recognise remaining the perfect square trinomial to find:

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

Explanation:

x^3-18x^2+81x = x(x^2-18x+81)

We can recognise x^2-18x+81 as being a perfect square trinomial, as it is of the form a^2-2ab+b^2 = (a-b)^2 with a=x and b=9.

Thus:

x^3-18x^2+81x

= x(x^2-18x+81)

= x(x^2-(2*x*9)+9^2)

= x(x-9)^2