Solve a(a-1)(a-2)(a-3)

$$a ( a - 1 ) ( a - 2 ) ( a - 3 )$$

Evaluate

$$a\left(a-3\right)\left(a-2\right)\left(a-1\right)$$

Solution Steps

Use the distributive property to multiply a by a-1.

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

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

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

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

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

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

$$a^{4}-3a^{3}-3a^{3}+9a^{2}+2a^{2}-6a$$

Combine -3a^{3} and -3a^{3} to get -6a^{3}.

$$a^{4}-6a^{3}+9a^{2}+2a^{2}-6a$$

Combine 9a^{2} and 2a^{2} to get 11a^{2}.

$$a^{4}-6a^{3}+11a^{2}-6a$$

Expand

$$a^{4}-6a^{3}+11a^{2}-6a$$

Solution Steps

Use the distributive property to multiply a by a-1.

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

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

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

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

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

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

$$a^{4}-3a^{3}-3a^{3}+9a^{2}+2a^{2}-6a$$

Combine -3a^{3} and -3a^{3} to get -6a^{3}.

$$a^{4}-6a^{3}+9a^{2}+2a^{2}-6a$$

Combine 9a^{2} and 2a^{2} to get 11a^{2}.

$$a^{4}-6a^{3}+11a^{2}-6a$$