Question

Completely factor the expression:
112x^2-567y^2

Could you show me the prime factorizations? What do they both go into, if I can figure this out I can do the rest, so please do not tell me the answer yet.

Answer 1

What I have so far is they both go into 7
112=7*16
567= 7*81

Answer 2

If this is the right combination, then how do I set that up, I know I know how to do this it is just not coming to me.

would it be
(7x-16y)(7x-81y)

Answer 3

\[7(16x^2 - 81y^2) = 7(4x + 9y)(4x-9y)\]

Answer 4

That is the answer? Can you show your work.

Answer 5

Why can it not be wrote like this7(16x-81y)^2 ?

Answer 6

Because of the binomial theorem. \[(a-b)*(a+b) = a^2 -a*b + a*b - b^2\]

Answer 7

How do you work it out with this theorem? what is a and what is b?

Answer 8

a and b are just variables. You did a good job factoring out the common factor of 7. After that, you factor what is called a difference of squares. 16 is 4 squared and 81 is 9 squared. 4 = a and 9 = b in this case. If you plug in those numbers you will see that my formula matches your question.

Answer 9

Ok, lets do it, give me a minute.

Answer 10

(a-b)*(a+b)=a^2-a * b+a*b-b^2
(4-9) * (4+9)=4^2-4 *9+4*9-9^2
-5*13=16-4*9+4*9- 81
-65=12*9
-65=108+4*9-81
-65=112*9-81
-65=1008-81
-65=927


This is what I have, but it doesnt seem right. I used PEMDAS to calculate it.

Answer 11

wat did you do....

16 - 81 = -5*13....
-4*9 + 4*9 = 0

Answer 12

PEMDAS is ORDER of operations. MEANING you do MULTIPLICATION and DIVISION BEFORE BEFORE BEFORE addition and subtraction. What grade are you in?

Answer 13

I did it in order, It wasn't coming out = so I didn't think it was right.
I did the exponents first. Well you dont have to be so mean about it!

Answer 14

(a-b)*(a+b)=a^2-a * b+a*b-b^2
(4-9) * (4+9)=4^2-4 *9+4*9-9^2
-5*13=16-4*9+4*9-81
-65=16-|-144+36-81
-65=160+36-81
-65=196-81
-65=115

It still did not= out.
If you are going to have an attitude towards helping me, you don't have to I will repost it and get help from someone else!

Answer 15

\[(4-9)*(4+9) =(4^2) + (- 4*9) + (4*9) - (9^2) = -65 = -5*13\]
I'm using Capitals to emphasize my point. And I was seriously asking what grade you are in, I'm a Sophomore in College, I want to know how much math you have taken.