# How do you factor 9x^2-24x+16?

Jun 5, 2015

This is a perfect square trinomial.

It can be recognised because it is of the form:

${a}^{2} - 2 a b + {b}^{2} = {\left(a - b\right)}^{2}$

with $a = 3 x$ and $b = 4$

$9 {x}^{2} - 24 x + 16 = {\left(3 x\right)}^{2} - \left(2 \cdot \left(3 x\right) \cdot 4\right) + {4}^{2}$

$= {\left(3 x - 4\right)}^{2}$