(x+2y)^3
facor please

Question

(x+2y)^3
facor please

solomonzelman · Answer

$$x^3+6x^2y+8y^2x+8y^3$$

Need more help understanding?

anonymous · Answer

Yes, explain please

solomonzelman · Answer

|dw:1380787232617:dw| do you know what this is?

anonymous · Answer

yes....

solomonzelman · Answer

so for example $$(a+b)^3 $$ to factor this out u would do the following:

solomonzelman · Answer

$$ a^3+a^2b+ab^2+b^3$$
OK?

anonymous · Answer

than what?

solomonzelman · Answer

Substitute x for a, and  2y for  b and work it out!

anonymous · Answer

OK, but where do u get that from?

solomonzelman · Answer

What? the$$a^3+a^2b+ab^2+b^3$$ ?

anonymous · Answer

yes!

solomonzelman · Answer

do u know what a polynomial is?

anonymous · Answer

yes, OK!

solomonzelman · Answer

So each in each polynomial if you were to add the powers of a to the powers of b, u would get 3, understand?

anonymous · Answer

Yes, and how did you get this specific equation

solomonzelman · Answer

Do u know there are four polynomials?

anonymous · Answer

Yes.....
can you tell me how you got the powers?

solomonzelman · Answer

1) there are (exactly) 4 polynomials
2) the sum of powers is the same (except that the power of one variable goes up when the power of the other decrease) (all sums of powers to get 3 are used: 3+0, 2+1, 1+2, 0+3)
this is the pattern the powers use
and when you get the equation w/ a 7 b plug in x for a and 2y for b.
Get it?

(Please, medal.....)

anonymous · Answer

Uh now I get it the key thing I was looking for is the "Pattern"
so for (a+b)^4 u would get    a^4    +    a^3 b   +    a^2 b^2   +   a b^3  +  b^4 ....
Tnx! here is your medal!