Is $9 x^{2} - 6 x + 1$ $9x^2 − 6x + 1$ a perfect square trinomial and how do you factor it?

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Answer 1 · 2015-06-03T19:51:32

Yes.

$9 x^{2} - 6 x + 1 = {(3 x)}^{2} - (2 \times 3 x \times 1) + 1^{2} = {(3 x - 1)}^{2}$ $9x^2-6x+1 = (3x)^2-(2xx3x xx1)+1^2 = (3x-1)^2$

You can recognise a perfect square trinomial as it takes the form:

$A^{2} \pm 2 A B + B^{2} = {(A \pm B)}^{2}$ $A^2+-2AB+B^2 = (A+-B)^2$

Is 9x^2 − 6x + 19x2−6x+19x^2 − 6x + 1 a perfect square trinomial and how do you factor it?