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

$$2 a ( a - b ) - b ( 2 a - b ) + 2 a b$$

Evaluate

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

Solution Steps

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

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

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

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

To find the opposite of 2ba-b^{2}, find the opposite of each term.

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

The opposite of -b^{2} is b^{2}.

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

Combine -2ab and -2ba to get -4ab.

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

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

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

Expand

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

Solution Steps

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

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

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

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

To find the opposite of 2ba-b^{2}, find the opposite of each term.

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

The opposite of -b^{2} is b^{2}.

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

Combine -2ab and -2ba to get -4ab.

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

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

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