What's 9k power of 2 minus 12k plus 4

12a(2)b(2)-27a(2)

IN THE BRACKETS ARE THE POWERS

Ok, here's your question:

9k^2 -12k +4

Give the factors of +4 (this is like trial and error)
They are +1, +2, +4 but also -1, -2, -4.

Now, factors of 9, which are +1, +3, +9 (no need to find negative factors here)

Write them in a certain form, like for example this one;

9k^2OOOOOO4
kOOOOOOO+1OOOOOO+9k
9kOOOOOO+4OOOOOO+4kOOOOOO
OOOOOOOOOOOOOOOO+13k

You obtain +13k when you add the products of 9k and +1, and k and +4. You need to obtain -12k.

By trying different numbers, you'll see that the answer is from;

9k^2OOOOOO4
3kOOOOOO-2OOOOOO-6k
3kOOOOOO-2OOOOOO-6kOOOOOO
OOOOOOOOOOOOOOOO-12k

And you factors will be (3k-2)(3k-2)

I know this may be a little confusing, there are several methods, and that's the one I was taught. Post back if you don't understand.

12a(2)b(2)-27a(2)

IN THE BRACKETS ARE THE POWERS

Here's your question;

12a^2b^2 - 27a^2

That's more simple than the previous one;

what are the common factors in 12a^2b^2 and 27a^2?

You'll find them be 3a^2, so factorise by that term and put what remains into brackets;

3a^2(4b^2 - 9)

You'll find your original question if you expand. Now, it happens that the terms in brackets are perfect squares, 4, b^2 and 9. From your formula of (a-b)(a+b) = a^2 - b^2, further factorise to give;

3a^2(2b+3)(2b-3)