Difference of squares

[K.I.L.E.R]

Remember the stupid ass formulas:

x^2 + y^2 = (x + y) * (x - y)
x^3 + y^2 - z = ?

etc...

How do you work backwards?
I never really understood how to work backwards on the more complex algebra which has caused problems for me my entire life.
Can someone please explain this?

Yes, I've searched Google but they only show silly formulas. Not very helpful for someone who wants to do this via hand and without memorisation.

I'm stuck:
(x + y^2)(x + z) = x^2 + xz + xy^2 + zy^2

Going backwards (Taking out common factors):
x(x+z) + y^2(x + z)

Now I'm stuck.

My original problem:
Solve for t:

P^2 + 2PtD + tD^2 - r^2 = 0

I'm trying to do this without quadratic formula. I just don't know how to get 't' alone.

 

[nintenho]

FOIL

First
Outer
Inner
Last

I forgot how to do your problem. There was a specific step that I always forgot.

 

[K.I.L.E.R]

I got:

t = (r^2 - P^2) / (2DP + 2D^2 - D^2)

cleaned up:

t = (r^2 - P^2) / D(2P + D)

Assumption:
t = 0, 1 intersection
t > 1 = multiple intersection
t < 1 = no intersections?

Oops. I just noticed.
A scalar cannot equal a vector.

What would happen if I arranged this into dot products?
t = r^2 - P.P / D.(2P + D)

 

[davepermen]

I'm stuck:
(x + y^2)(x + z) = x^2 + xz + xy^2 + zy^2

Going backwards (Taking out common factors):
x(x+z) + y^2(x + z)

Now I'm stuck.

if you look at this, you should see that in front of your (x+z), you have 'x' and ' + y^2'. together, they just build up your other term, (x + y^2).

and, to do it in steps.. once you got your (x+z), replace it with something.. say

a = x+z

=>

x*a + y^2*a

or

ax + ay^2

and then, again, take out the common term, in this case, a

a(x+y^2)

now substitute back x+z = a

(x+z)(x+y^2)


mostly, it's similar to search-and-replace

hope that helps as an idea

 

[Simon F]

Remember the stupid ass formulas:

x^2 + y^2 = (x + y) * (x - y)

There's nothing "stupid arse" about it... except that you wrote it incorrectly!

You want

x^2 [B][I]-[/I][/B] y^2 = (x + y) * (x - y)

Incidentally, this has been used to factor large numbers as in the QR Sieve.