Evaluate
\left(x^{2}+x+1\right)\left(x^{4}+x^{3}+x^{2}+x+1\right)
Expand
x^{6}+2x^{5}+3x^{4}+3x^{3}+3x^{2}+2x+1
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x^{6}+2x^{5}+3x^{4}+4x^{3}+3x^{2}+2x+1-x^{3}
Square 1+x+x^{2}+x^{3}.
x^{6}+2x^{5}+3x^{4}+3x^{3}+3x^{2}+2x+1
Combine 4x^{3} and -x^{3} to get 3x^{3}.
x^{6}+2x^{5}+3x^{4}+4x^{3}+3x^{2}+2x+1-x^{3}
Square 1+x+x^{2}+x^{3}.
x^{6}+2x^{5}+3x^{4}+3x^{3}+3x^{2}+2x+1
Combine 4x^{3} and -x^{3} to get 3x^{3}.
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