Question

Is 9x^2 - 12x + 4 a perfect square? Why?

Answer 1

Because it is equal to (3x - 2)^2.

Explanation:

If we factor we'll see why:

9x^2 - 12x + 4

To factor we can use the 'ac' method:

Multiplying the leading coefficient by the constant term: 9 * 4 = 36.

We need 2 numbers whose product is 36 and whose sum is -12:

These are -6 and -6 so we write:

9x^2 - 6x - 6x + 4

Factor by grouping:

= 3x(3x - 2) - 2(3x - 2)

= (3x - 2)(3x - 2)

= (3x - 2)^2 which is a perfect square.

Answer 2

Yes

Explanation:

9x^2-12x+4 can be factored to (3x-2)(3x-2). If you use the FOIL method, 3x times 3x gives you 9x^2, 3x times -2 gives you -6x, -2 times 3x gives you -6x (-6x + -6x gives you -12), and lastly -2 times -2 gives you 4.