Simple Algebra Help? Answer fast and prove how much smarter than me you are!!!?

Question

How do you perform/what is the equation for the sum of squares?
Example: Factor x^2+y^2

Also, factor x^2-5x+15

2x^2-8x+5

6pr^2 - pw^2 - 3rw + 2p^2rw

a^2bc - ab^2d + ac^2d - bcd^2

Answer 1

The first three can't be factored in real terms. (THAT is what "factoring" means; imaginary "factorings," though they may be possible, are not generally considered solutions to a problem posed as "Factorize the following.")

#4. 6pr^2 - pw^2 - 3rw + 2p^2rw = 2pr(3r + pw) - w(3r + pw)

= (2pr - w)(3r + pw).

#5. a^2bc - ab^2d + ac^2d - bcd^2 = ab(ac - bd) + cd(ac - bd)

= (ab + cd) (ac - bd).

[Note : This is NOT expressible as the difference of two squares. I'm afraid that the next responder must have misread or mistyped his penultimate step.]

Where did you get these ?!

Answer 2

1. x^2 + y^2 = (x + yi)(x - yi)....where i = root of -1...

2. x^2 - 5x + 15 = (x - (5+35i)/2)(x - (5-35i)/2)...refer to above

3. 2x^2 - 8x + 5 = (x - 4+root(11)/2)(x - 4-root(11)/2)

4. 6pr^2 - pw^2 - 3rw + 2p^2rw = 3r(2pr - w) + pw(2pr - w) = (3r + pw)(2pr - w)

5. a^2bc - ab^2d + ac^2d - bcd^2 = ab(ac - bd) + cd(ac - bd) = (ab + cd)(ab - cd) or a^2b^2 - c^2d^2 however you want it...

Answer 3

Might not be smarter, but I remember my algebra because I always did my own homework. So I still know it!

Might be smarter, too.