Question 631629
(x+y+z)^3

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

We multiply using the FOIL Method:

x * x = x^2

x * y = xy

x * z = xz

y * x = xy

y * y = y^2

y * z = yz

z * x = xz

z * y = yz

z * z = z^2

We now have:

x^2 + xy + xz + xy + y^2 + yz + xz + yz + z^2

Combine like terms:

xy + xy =2xy

xz + xz = 2xz

yz + yz = 2yz

Therefore:

x^2 + y^2 + z^2 + 2xy + 2xz + 2yz

(x^2 y^2 + z^2 + 2xy + 2xz + yz)(x + y + z)

x^2 * x = x^3

x^2 * y = x^2y

x^2 * z = x^2z

y^2 * x = y^2x

y^2 * y = y^3

y^2 * z = y^2z

z^2 * x = z^2x

z^2 * y = z^2y

z^2 * z = z^3

2xy * x = 2x^2y

2xy * y = 2y^2x

2xy * z = 2xyz

2xz * x = 2x^2z

2xz * y = 2xyz

2xz * z = 2z^2x

2yz * x = 2xyz

2yz * y = 2y^2z

2yz * z = 2z^2y

We now have:

x^3 + x^2y + x^2z + y^3 + y^2x + y^2z

+ z^3 + z^2y + z^2x + 2x^2y + 2xy^2 + 2xyz

+ 2x^2z + 2xyz + 2z^2x + 2xyz + 2y^2z + 2z^2y

Combine like terms:

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

2xy^2 + xy^2 = 3xy^2

2xyz + 2xyz + 2xyz = 6xyz

2x^2z + x^z = 3x^2z

2z^2x + z^2x = 3z^2x

2y^2z + y^2z = 3y^2z

2z^2y + z^2y = 3z^2y


The Answer:


x^3 + y^3 + z^3 + 3x^2y + 3xy^2

+ 3x^2z + 3z^2x + 3y^2z + 3z^2y + 6xyz




Lennox Obuong
Algebra Student
Email: obuong3@aol.com