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

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

Evaluate

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

Solution Steps

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

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

Combine a^{2} and -a^{2} to get 0.

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

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

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

Expand

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

Solution Steps

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

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

Combine a^{2} and -a^{2} to get 0.

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

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

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