Solve (n-2)(n+3)(n+5)

$$( n - 2 ) ( n + 3 ) ( n + 5 )$$

Expand

$$n^{3}+6n^{2}-n-30$$

Solution Steps

Apply the distributive property by multiplying each term of n-2 by each term of n+3.

$$\left(n^{2}+3n-2n-6\right)\left(n+5\right)$$

Combine 3n and -2n to get n.

$$\left(n^{2}+n-6\right)\left(n+5\right)$$

Apply the distributive property by multiplying each term of n^{2}+n-6 by each term of n+5.

$$n^{3}+5n^{2}+n^{2}+5n-6n-30$$

Combine 5n^{2} and n^{2} to get 6n^{2}.

$$n^{3}+6n^{2}+5n-6n-30$$

Combine 5n and -6n to get -n.

$$n^{3}+6n^{2}-n-30$$

Evaluate

$$\left(n-2\right)\left(n+3\right)\left(n+5\right)$$

Solution Steps

Apply the distributive property by multiplying each term of n-2 by each term of n+3.

$$\left(n^{2}+3n-2n-6\right)\left(n+5\right)$$

Combine 3n and -2n to get n.

$$\left(n^{2}+n-6\right)\left(n+5\right)$$

Apply the distributive property by multiplying each term of n^{2}+n-6 by each term of n+5.

$$n^{3}+5n^{2}+n^{2}+5n-6n-30$$

Combine 5n^{2} and n^{2} to get 6n^{2}.

$$n^{3}+6n^{2}+5n-6n-30$$

Combine 5n and -6n to get -n.

$$n^{3}+6n^{2}-n-30$$