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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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