Evaluate
\left(x-7\right)\left(x^{2}-5x+13\right)
Expand
x^{3}-12x^{2}+48x-91
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x^{3}-12x^{2}+48x-64-27
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-4\right)^{3}.
x^{3}-12x^{2}+48x-91
Subtract 27 from -64 to get -91.
x^{3}-12x^{2}+48x-64-27
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-4\right)^{3}.
x^{3}-12x^{2}+48x-91
Subtract 27 from -64 to get -91.
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