How do you know if 9x^2 +12x - 4 is a perfect square trinomial and how do you factor it?

1 Answer
Jun 7, 2015

color(blue)(9x^2) is a perfect square : =color(blue)((3x)^2)
color(red)4 is also a perfect square : =color(red)(2^2)
And color(purple)(12x)=2*color(blue)(3x)*color(red)2

We know that (color(blue)a-color(red)b)²=color(blue)(a^2)-2color(blue)acolor(red)b+color(red)(b^2)
And (color(blue)a+color(red)b)²=color(blue)(a^2)+2color(blue)acolor(red)b+color(red)(b^2)

But here we have color(blue)(a^2)+2color(blue)acolor(red)b-color(red)(b^2)

This isn't a perfect square trinomial, so we can't factor it.