Quick squaring question (1 Viewer)

[Volarath]

(x + y + z)² = ???

I seem to recall some pyramidal pattern for doing these things...

Any help appreciated.

 

[volition]

I think its:
2 (xy + xz+ yz) + x^2 + y^2 + z^2

kinda like two times the products of the thing plus the squares of each one individually

 

[SoulSearcher]

I think its:
2 (xy + xz+ yz) + x^2 + y^2 + z^2

kinda like two times the products of the thing plus the squares of each one individually

That's correct.

 

[Slidey]

What about (x+y+z)^3? What about 4, 5...?

There is a pattern much like the binomial theorem. Can you find it?

 

[Wackedupwacko]

o its not a hard thing

(x+y+z)³
= 1(x³+y³+z³) + 3(x²y+x²z+y²x+y²z+z²x+z²y)+3(xyz)

similar to binomial theorem

eg (x+y+z)^4

1(x^4+y^4+z^4) + 4(1 cube term 1 other) +6(2square terms) +4(1square an the other 2)

etc etc