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

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

Evaluate

$$\left(a-b\right)\left(3a-2b\right)$$

Solution Steps

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

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

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

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

Combine -4ab and -ab to get -5ab.

$$2a^{2}-5ab+2b^{2}+a^{2}$$

Combine 2a^{2} and a^{2} to get 3a^{2}.

$$3a^{2}-5ab+2b^{2}$$

Expand

$$3a^{2}-5ab+2b^{2}$$

Solution Steps

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

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

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

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

Combine -4ab and -ab to get -5ab.

$$2a^{2}-5ab+2b^{2}+a^{2}$$

Combine 2a^{2} and a^{2} to get 3a^{2}.

$$3a^{2}-5ab+2b^{2}$$