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

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

Evaluate

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

Solution Steps

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

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

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

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

Expand

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

Solution Steps

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

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

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

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