Evaluate
\left(x-1\right)\left(x^{2}-5x+7\right)
Expand
x^{3}-6x^{2}+12x-7
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x^{3}-6x^{2}+12x-8+1
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-2\right)^{3}.
x^{3}-6x^{2}+12x-7
Add -8 and 1 to get -7.
x^{3}-6x^{2}+12x-8+1
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-2\right)^{3}.
x^{3}-6x^{2}+12x-7
Add -8 and 1 to get -7.
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