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

Question

How do you expand (x+y)^3?

Answer 1

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!!

Answer 2

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

Answer 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

Answer 4

= (x + y)³

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

= (x² + xy + xy + y²)(x + y)

= (x² + 2x + y²)(x + y)

= x³ + 2x² + xy² + x²y + 2xy + y³

= x³ + 2x² + xy² + x²y + 2xy + y³

Answer: x³ + 2x² + xy² + x²y + 2x + y³

Answer 5

(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

Answer 6

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.

Answer 7

According to identities

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

if you are an INDIAN you must be knowing this!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 8

(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                          

Answer 9

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

          =(x^2+2xy+y^2)(x+y)

          =(x^3+3x^2y+3xy^2+y^3)

Answer 10

( 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