How do you factor $9 x^{2} - 24 x + 16$ $9x^2-24x+16$ ?

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Answer 1 · 2015-06-05T22:01:44

This is a perfect square trinomial.

It can be recognised because it is of the form:

$a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ $a^2-2ab+b^2 = (a-b)^2$

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

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

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

How do you factor 9x^2-24x+169x2−24x+169x^2-24x+16?