Evaluate
\left(x-4\right)\left(\left(x-4\right)^{2}-2\right)
Expand
x^{3}-12x^{2}+46x-56
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x^{3}-12x^{2}+48x-64-2\left(x-4\right)
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-64-2x+8
Use the distributive property to multiply -2 by x-4.
x^{3}-12x^{2}+46x-64+8
Combine 48x and -2x to get 46x.
x^{3}-12x^{2}+46x-56
Add -64 and 8 to get -56.
x^{3}-12x^{2}+48x-64-2\left(x-4\right)
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-64-2x+8
Use the distributive property to multiply -2 by x-4.
x^{3}-12x^{2}+46x-64+8
Combine 48x and -2x to get 46x.
x^{3}-12x^{2}+46x-56
Add -64 and 8 to get -56.
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