Solve a*(a-2)-(a+2)^2-2a*(a-4)=

$$a \cdot ( a - 2 ) - ( a + 2 ) ^ { 2 } - 2 a \cdot ( a - 4 ) =$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

$$-2a-4a-4-2a\left(a-4\right)$$

Combine -2a and -4a to get -6a.

$$-6a-4-2a\left(a-4\right)$$

Use the distributive property to multiply -2a by a-4.

$$-6a-4-2a^{2}+8a$$

Combine -6a and 8a to get 2a.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

$$-2a-4a-4-2a\left(a-4\right)$$

Combine -2a and -4a to get -6a.

$$-6a-4-2a\left(a-4\right)$$

Use the distributive property to multiply -2a by a-4.

$$-6a-4-2a^{2}+8a$$

Combine -6a and 8a to get 2a.

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