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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-2\right)^{2}.

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

To find the opposite of a^{2}-4a+4, find the opposite of each term.

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

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

$$-2a+4a-4$$

Combine -2a and 4a to get 2a.

$$2a-4$$

Expand

$$2a-4$$

Solution Steps

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

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

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

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

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

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

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-2\right)^{2}.

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

To find the opposite of a^{2}-4a+4, find the opposite of each term.

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

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

$$-2a+4a-4$$

Combine -2a and 4a to get 2a.

$$2a-4$$