# Multiply (r+g)(r^2-rg+g^2) (r+g)(r2-rg+g2)
Expand (r+g)(r2-rg+g2) by multiplying each term in the first expression by each term in the second expression.
r⋅r2+r(-rg)+rg2+gr2+g(-rg)+g⋅g2
Simplify terms.
Simplify each term.
Multiply r by r2 by adding the exponents.
Multiply r by r2.
Raise r to the power of 1.
r1r2+r(-rg)+rg2+gr2+g(-rg)+g⋅g2
Use the power rule aman=am+n to combine exponents.
r1+2+r(-rg)+rg2+gr2+g(-rg)+g⋅g2
r1+2+r(-rg)+rg2+gr2+g(-rg)+g⋅g2
r3+r(-rg)+rg2+gr2+g(-rg)+g⋅g2
r3+r(-rg)+rg2+gr2+g(-rg)+g⋅g2
Rewrite using the commutative property of multiplication.
r3-r(rg)+rg2+gr2+g(-rg)+g⋅g2
Multiply r by r by adding the exponents.
Move r.
r3-(r⋅r)g+rg2+gr2+g(-rg)+g⋅g2
Multiply r by r.
r3-r2g+rg2+gr2+g(-rg)+g⋅g2
r3-r2g+rg2+gr2+g(-rg)+g⋅g2
Rewrite using the commutative property of multiplication.
r3-r2g+rg2+gr2-g(rg)+g⋅g2
Multiply g by g by adding the exponents.
Move g.
r3-r2g+rg2+gr2-(g⋅g)r+g⋅g2
Multiply g by g.
r3-r2g+rg2+gr2-g2r+g⋅g2
r3-r2g+rg2+gr2-g2r+g⋅g2
Multiply g by g2 by adding the exponents.
Multiply g by g2.
Raise g to the power of 1.
r3-r2g+rg2+gr2-g2r+g1g2
Use the power rule aman=am+n to combine exponents.
r3-r2g+rg2+gr2-g2r+g1+2
r3-r2g+rg2+gr2-g2r+g1+2
r3-r2g+rg2+gr2-g2r+g3
r3-r2g+rg2+gr2-g2r+g3
r3-r2g+rg2+gr2-g2r+g3
Combine the opposite terms in r3-r2g+rg2+gr2-g2r+g3.
Reorder the factors in the terms -r2g and gr2.
r3-r2g+rg2+r2g-g2r+g3
r3+rg2+0-g2r+g3
r3+rg2-g2r+g3
Reorder the factors in the terms rg2 and -g2r.
r3+g2r-g2r+g3
Subtract g2r from g2r.
r3+0+g3
r3+g3
r3+g3
r3+g3
Multiply (r+g)(r^2-rg+g^2)     