Solve (n-3)^3*(n+2)^2

$$( n - 3 ) ^ { 3 } \cdot ( n + 2 ) ^ { 2 }$$

Evaluate

$$\left(n+2\right)^{2}\left(n-3\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(n-3\right)^{3}.

$$\left(n^{3}-9n^{2}+27n-27\right)\left(n+2\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+2\right)^{2}.

$$\left(n^{3}-9n^{2}+27n-27\right)\left(n^{2}+4n+4\right)$$

Use the distributive property to multiply n^{3}-9n^{2}+27n-27 by n^{2}+4n+4 and combine like terms.

$$n^{5}-5n^{4}-5n^{3}+45n^{2}-108$$

Expand

$$n^{5}-5n^{4}-5n^{3}+45n^{2}-108$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(n-3\right)^{3}.

$$\left(n^{3}-9n^{2}+27n-27\right)\left(n+2\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+2\right)^{2}.

$$\left(n^{3}-9n^{2}+27n-27\right)\left(n^{2}+4n+4\right)$$

Use the distributive property to multiply n^{3}-9n^{2}+27n-27 by n^{2}+4n+4 and combine like terms.

$$n^{5}-5n^{4}-5n^{3}+45n^{2}-108$$