Evaluate
\left(U+5\right)\left(U^{2}+4U+7\right)
Expand
U^{3}+9U^{2}+27U+35
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U^{3}+9U^{2}+27U+27+8
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(U+3\right)^{3}.
U^{3}+9U^{2}+27U+35
Add 27 and 8 to get 35.
U^{3}+9U^{2}+27U+27+8
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(U+3\right)^{3}.
U^{3}+9U^{2}+27U+35
Add 27 and 8 to get 35.
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