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

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

Evaluate

$$a\left(a^{3}-4a^{2}+11\right)$$

Solution Steps

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

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

Use the distributive property to multiply a^{2}-a by a^{2}-a+1 and combine like terms.

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

Use the distributive property to multiply -2a by a-2.

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

Use the distributive property to multiply -2a^{2}+4a by a+3 and combine like terms.

$$a^{4}-2a^{3}+2a^{2}-a-2a^{3}-2a^{2}+12a$$

Combine -2a^{3} and -2a^{3} to get -4a^{3}.

$$a^{4}-4a^{3}+2a^{2}-a-2a^{2}+12a$$

Combine 2a^{2} and -2a^{2} to get 0.

$$a^{4}-4a^{3}-a+12a$$

Combine -a and 12a to get 11a.

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

Expand

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

Solution Steps

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

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

Use the distributive property to multiply a^{2}-a by a^{2}-a+1 and combine like terms.

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

Use the distributive property to multiply -2a by a-2.

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

Use the distributive property to multiply -2a^{2}+4a by a+3 and combine like terms.

$$a^{4}-2a^{3}+2a^{2}-a-2a^{3}-2a^{2}+12a$$

Combine -2a^{3} and -2a^{3} to get -4a^{3}.

$$a^{4}-4a^{3}+2a^{2}-a-2a^{2}+12a$$

Combine 2a^{2} and -2a^{2} to get 0.

$$a^{4}-4a^{3}-a+12a$$

Combine -a and 12a to get 11a.

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