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

$$( a - 1 ) ( a + 3 ) ( 2 - a ) + ( a ^ { 2 } + a + 2 ) ( a - 3 )$$

Evaluate

$$-2a^{2}+6a-12$$

Solution Steps

Use the distributive property to multiply a-1 by a+3 and combine like terms.

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

Use the distributive property to multiply a^{2}+2a-3 by 2-a and combine like terms.

$$-a^{3}+7a-6+\left(a^{2}+a+2\right)\left(a-3\right)$$

Use the distributive property to multiply a^{2}+a+2 by a-3 and combine like terms.

$$-a^{3}+7a-6+a^{3}-2a^{2}-a-6$$

Combine -a^{3} and a^{3} to get 0.

$$7a-6-2a^{2}-a-6$$

Combine 7a and -a to get 6a.

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

Subtract 6 from -6 to get -12.

$$6a-12-2a^{2}$$

Expand

$$-2a^{2}+6a-12$$

Solution Steps

Use the distributive property to multiply a-1 by a+3 and combine like terms.

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

Use the distributive property to multiply a^{2}+2a-3 by 2-a and combine like terms.

$$-a^{3}+7a-6+\left(a^{2}+a+2\right)\left(a-3\right)$$

Use the distributive property to multiply a^{2}+a+2 by a-3 and combine like terms.

$$-a^{3}+7a-6+a^{3}-2a^{2}-a-6$$

Combine -a^{3} and a^{3} to get 0.

$$7a-6-2a^{2}-a-6$$

Combine 7a and -a to get 6a.

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

Subtract 6 from -6 to get -12.

$$6a-12-2a^{2}$$