Solve (a-4)(a+1)(a-5)

$$( a - 4 ) ( a + 1 ) ( a - 5 )$$

Evaluate

$$\left(a-5\right)\left(a-4\right)\left(a+1\right)$$

Solution Steps

Apply the distributive property by multiplying each term of a-4 by each term of a+1.

$$\left(a^{2}+a-4a-4\right)\left(a-5\right)$$

Combine a and -4a to get -3a.

$$\left(a^{2}-3a-4\right)\left(a-5\right)$$

Apply the distributive property by multiplying each term of a^{2}-3a-4 by each term of a-5.

$$a^{3}-5a^{2}-3a^{2}+15a-4a+20$$

Combine -5a^{2} and -3a^{2} to get -8a^{2}.

$$a^{3}-8a^{2}+15a-4a+20$$

Combine 15a and -4a to get 11a.

$$a^{3}-8a^{2}+11a+20$$

Expand

$$a^{3}-8a^{2}+11a+20$$

Solution Steps

Apply the distributive property by multiplying each term of a-4 by each term of a+1.

$$\left(a^{2}+a-4a-4\right)\left(a-5\right)$$

Combine a and -4a to get -3a.

$$\left(a^{2}-3a-4\right)\left(a-5\right)$$

Apply the distributive property by multiplying each term of a^{2}-3a-4 by each term of a-5.

$$a^{3}-5a^{2}-3a^{2}+15a-4a+20$$

Combine -5a^{2} and -3a^{2} to get -8a^{2}.

$$a^{3}-8a^{2}+15a-4a+20$$

Combine 15a and -4a to get 11a.

$$a^{3}-8a^{2}+11a+20$$