How do you do (X+y)^3? ?

You can use the formula method, or expand it by hand:

(x + y)(x + y)(x + y)

= (x^2 + 2xy + y^2)(x + y)

= x^3 + 2x^2y +xy^2 + x^2y + 2xy^2 + y^3

= x^3 + 3x^2y + 3xy^2 + y^3

Can't remember the formula, so I usually do it by hand.

(x + y) ^3 = x^3 + 3 x^2 y + 3 x y^2 + y^3

coefficients are: C(3,0), C(3,1), C(3,2), C(3,3)

or

use Pascal triangle for coefficients:

1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

( x + y ) ( x ² + 2 x y + y ² )

x ³ + 2 x ² y + x y ²
_____x ² y + 2 x y ² + y ³

x ³ + 3 x ² y + 3 x y ² + y ³

You assemble like words. 3y + x - 2x + y3 + x + x 3y + y3 = 6y x - 2x + x +x = x = x + 6y this could be D. besides the undeniable fact that it is erroneous. y3 and 3y are the comparable element because of the fact it particularly is y x 3 and 3 x y.

(x + y)^3
= (x + y)(x + y)(x + y)
= (x*x + y*x + x*y + y*y)(x + y)
= (x^2 + xy + xy + y^2)(x + y)
= (x^2 + 2xy + y^2)(x + y)
= x^2*x + 2xy*x + y^2*x + x^2*y + 2xy*y + y^2*y
= x^3 + 2x^2y + xy^2 + x^2y + 2xy^2 + y^3
= x^3 + 2x^2y + x^2y + xy^2 + 2xy^2 + y^3
= x^3 + 3x^2y + 3xy^2 + y^3

According to identities
(x+y)^3 = x^3+y^3+3xy(x+y)
if you are an INDIAN you must be knowing this!!!!!!!!!!!!!!!!!!!!!!!!!!!

You have to do one step at a time. What I mean by this is write it out first. You know that an exponent means how many times that quantity is multiplied by itself, right? Well lets go ahead and apply that knowledge:

(x + y)(x + y)(x + y)

Now, FOIL the first two quantities (First Outter Inner Last):

(x^2 + 2xy + y^2)(x + y)

Now, multiply what you have left. All you have to do is distribute the x and y separately:

(x^3 + 2(x^2)y + xy^2) plus (yx^2 + 2xy^2 + y^3)

Combine like terms. These include:
2(x^2)y and yx^2
and
xy^2 and 2xy^2

So the final expanded answer is:

x^3 + y^3 + 3yx^2 + 3xy^2

I hope you understand!!

(x+y)^3=(x+y)^2(x+y)
=(x^2+2xy+y^2)(x+y)
=(x^3+3x^2y+3xy^2+y^3)

Hey,
(x+y)^3 = (x+y)^2(x+y)

expand (x+y)^2 = x^2+2xy+y^2

now multiply again

(x^2+2xy+y^2)(x+y) = x^3 +2x^2y+y^2x+yx^2+2xy^2+y^3

yes its a long answer

hope this helps

(x+y)(x+y)(x+y) or x^3+y^3