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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply -3 by ab-b^{2}.

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

Combine -2b^{2} and 3b^{2} to get b^{2}.

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

Combine b^{2} and b^{2} to get 2b^{2}.

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

Combine -3ab and -ab to get -4ab.

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

Expand

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

Solution Steps

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

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

Use the distributive property to multiply -3 by ab-b^{2}.

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

Combine -2b^{2} and 3b^{2} to get b^{2}.

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

Combine b^{2} and b^{2} to get 2b^{2}.

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

Combine -3ab and -ab to get -4ab.

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