Solve -(a+b)*(a-b)-a*(a-b)+2a^2

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

Evaluate

$$b\left(a+b\right)$$

Solution Steps

To find the opposite of a+b, find the opposite of each term.

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

Use the distributive property to multiply -a-b by a-b and combine like terms.

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

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

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

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

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

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

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

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

$$b^{2}+ab$$

Expand

$$ab+b^{2}$$

Solution Steps

To find the opposite of a+b, find the opposite of each term.

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

Use the distributive property to multiply -a-b by a-b and combine like terms.

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

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

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

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

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

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

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

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

$$b^{2}+ab$$