Question

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

Answer 1

`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.