Question 631629: (x+y+z)^3
Answer by lenny460(1073)   (Show Source):
You can put this solution on YOUR website! (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
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