i hate you, seemingly easy kiddie math.?

Question

can somebody please break it down and explain to me how you factor this: a squared - 2ab + b squared

and how do you simplifty 2x squared - 32 OVER x - 4 ?

oops, a typo...simplify*

Answer 1

It order to solve it, you are normally give what A and B equal.

Example: If A=2 and B=4, plug the numbers into the letters place.

2squared - 2(2)(4) + 4 squared.
Then using the rules of math, you solve the multipulcations first.

2 squared is 4
2(2)(4) is 16
4 squared is 16

Then solve the rest in order
4 - 16 = (-12) +16 = 4

I cant remember how to do the second problem. The "OVER" comment is lost to me right now

Answer 2

For a^2 - 2ab + b^2

You need to set up your two sets of parenthesis and the only way to get a^2 is a times a and the only way to get b^2 is b times b. Now for the sign on the 2ab term, if it is negative both parenthesis are minus and if it is positive both parenthesis are positive. The answer is (a-b)(a-b) or (a-b)^2



(2x^2 - 32)/(x-4)

factor 2x^2 -32;
GCF is 2
2(x^2-16)
x^2 - 16 is a difference of squares and factors into (x-4)(x+4)
completely factored you get 2(x-4)(x+4)
now rewrite the problem in factored form
[2(x-4)(x+4)]/x-4
Cancel the (x-4)'s
The answer is 2(x+4)

Answer 3

Well the first one is (a+b) quantity squared, or (a+b) (a+b) Remember FOIL - First, Outside, Inside, Last - so

a times a, then ab, then ab again, then b times b. Yielding a squared plus 2ab plus b squared.

The second one factors first into 2(x squared-16). Then the x squared -16 factors into (x+4) ( x-4) Again using FOIL, we have

x squared, plus 4x, minus 4x, +y squared.

So you get x (x+4) (x-4) over (x-4). The two (x-4)s cancel, leaving x(x+4)

That'll be a dollar. * smiles *