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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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