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

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

Evaluate

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

Solution Steps

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

$$\left(2a+a^{2}-6-3a\right)\left(1-a\right)$$

Combine 2a and -3a to get -a.

$$\left(-a+a^{2}-6\right)\left(1-a\right)$$

Apply the distributive property by multiplying each term of -a+a^{2}-6 by each term of 1-a.

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

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

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

Combine -a and 6a to get 5a.

$$5a+2a^{2}-a^{3}-6$$

Expand

$$-a^{3}+2a^{2}+5a-6$$

Solution Steps

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

$$\left(2a+a^{2}-6-3a\right)\left(1-a\right)$$

Combine 2a and -3a to get -a.

$$\left(-a+a^{2}-6\right)\left(1-a\right)$$

Apply the distributive property by multiplying each term of -a+a^{2}-6 by each term of 1-a.

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

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

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

Combine -a and 6a to get 5a.

$$5a+2a^{2}-a^{3}-6$$