Solve 2(p+3)-p^2-2p(2-p)-14=

$$2 ( p + 3 ) - p ^ { 2 } - 2 p ( 2 - p ) - 14 =$$

Evaluate

$$\left(p-4\right)\left(p+2\right)$$

Solution Steps

Use the distributive property to multiply 2 by p+3.

$$2p+6-p^{2}-2p\left(2-p\right)-14$$

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

$$2p+6-p^{2}-4p+2p^{2}-14$$

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

$$-2p+6-p^{2}+2p^{2}-14$$

Combine -p^{2} and 2p^{2} to get p^{2}.

$$-2p+6+p^{2}-14$$

Subtract 14 from 6 to get -8.

$$-2p-8+p^{2}$$

Expand

$$p^{2}-2p-8$$

Solution Steps

Use the distributive property to multiply 2 by p+3.

$$2p+6-p^{2}-2p\left(2-p\right)-14$$

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

$$2p+6-p^{2}-4p+2p^{2}-14$$

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

$$-2p+6-p^{2}+2p^{2}-14$$

Combine -p^{2} and 2p^{2} to get p^{2}.

$$-2p+6+p^{2}-14$$

Subtract 14 from 6 to get -8.

$$-2p-8+p^{2}$$