Help with HW???!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!????????

I only have these left and I can't figure them out-_-

Factor the expression

9x^2-81

Factor the trinomial

9x^2+24x+16

12x^2+46x-36

The first one is a difference of two perfect squares. That means that the 9, when square rooted is a whole number, the x^2 when square rooted is a whole variable, and 81, when square rooted is a whole number. So you take the square root of both terms and rewrite them like so...

(3x 9)(3x 9)

Now, all you need to do is add the + and - sign, and you're finished.

(3x+9)(3x-9). You can FOIL this to check your answer.

I would use the big X method to solve the other two. Draw an X on your paper (fairly big). At the top, write a*c, the bottom, write b, and then the two sides of the X, write #/a in each one.

This formula holds true for ax^2+bx+c.

Now to apply it to the problem...

The top of the X is 9*16 (a*c) which is 144. The bottom is 24, which was our b. We want two numbers that multiply together to get 144, but ADD up to 24. Well, it should be easy to see that 12*12 is 144 and 12+12 is 24. Now we write this number on the sides of our X where the #/a was.

Now, our number 12, has to be divided by a, which in this case is 12. So we write...

(x+12/9)(x+12/9) since those were the two numbers we found. SInce 9 doesn't go into 12 evenly, we move the 9 up front.

(9x+12)(9x+12). FOIL to check your answer.

Last one: This one is a little harder, but same concept. You are looking for two number that multiply to get 36, that add up to get 46. Or if you use the big x method, you are looking for two numbers that multiply to get 432, but add up to 46.

Try this one on your own. You should get an answer of (2x+9)(6x-4)

Others: SInce they have the same base, subtract the two exponents to get 5^2 = 25

1. First factor out the 9 and you get 9(x^2-9). Then you factor x^2-9 and you get (x+3)(x-3) so your final answer would be 9(x+3)(x-3)