Evaluate
\left(x+3\right)^{3}-x^{2}+27
Expand
x^{3}+8x^{2}+27x+54
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x^{3}+9x^{2}+27x+27-\left(x^{2}-27\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+3\right)^{3}.
x^{3}+9x^{2}+27x+27-x^{2}+27
To find the opposite of x^{2}-27, find the opposite of each term.
x^{3}+8x^{2}+27x+27+27
Combine 9x^{2} and -x^{2} to get 8x^{2}.
x^{3}+8x^{2}+27x+54
Add 27 and 27 to get 54.
x^{3}+9x^{2}+27x+27-\left(x^{2}-27\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+3\right)^{3}.
x^{3}+9x^{2}+27x+27-x^{2}+27
To find the opposite of x^{2}-27, find the opposite of each term.
x^{3}+8x^{2}+27x+27+27
Combine 9x^{2} and -x^{2} to get 8x^{2}.
x^{3}+8x^{2}+27x+54
Add 27 and 27 to get 54.
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Limits
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