Solve (a(a+b+2)-2(a^2+ab+2a)+3(a+ab))

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

Evaluate

$$a\left(1+2b-a\right)$$

Solution Steps

Use the distributive property to multiply a by a+b+2.

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

Use the distributive property to multiply -2 by a^{2}+ab+2a.

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

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

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

Combine ab and -2ab to get -ab.

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

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

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

Use the distributive property to multiply 3 by a+ab.

$$-a^{2}-ab-2a+3a+3ab$$

Combine -2a and 3a to get a.

$$-a^{2}-ab+a+3ab$$

Combine -ab and 3ab to get 2ab.

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

Expand

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

Solution Steps

Use the distributive property to multiply a by a+b+2.

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

Use the distributive property to multiply -2 by a^{2}+ab+2a.

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

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

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

Combine ab and -2ab to get -ab.

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

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

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

Use the distributive property to multiply 3 by a+ab.

$$-a^{2}-ab-2a+3a+3ab$$

Combine -2a and 3a to get a.

$$-a^{2}-ab+a+3ab$$

Combine -ab and 3ab to get 2ab.

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