Solve left(2pright)^2-left(2p-2qright)^2

$${ \left(2p \right) }^{ 2 } - { \left(2p-2q \right) }^{ 2 }$$

Evaluate

$$4q\left(2p-q\right)$$

Solution Steps

Expand \left(2p\right)^{2}.

$$2^{2}p^{2}-\left(2p-2q\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4p^{2}-\left(2p-2q\right)^{2}$$

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

$$4p^{2}-\left(4p^{2}-8pq+4q^{2}\right)$$

To find the opposite of 4p^{2}-8pq+4q^{2}, find the opposite of each term.

$$4p^{2}-4p^{2}+8pq-4q^{2}$$

Combine 4p^{2} and -4p^{2} to get 0.

$$8pq-4q^{2}$$

Expand

$$8pq-4q^{2}$$

Solution Steps

Expand \left(2p\right)^{2}.

$$2^{2}p^{2}-\left(2p-2q\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4p^{2}-\left(2p-2q\right)^{2}$$

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

$$4p^{2}-\left(4p^{2}-8pq+4q^{2}\right)$$

To find the opposite of 4p^{2}-8pq+4q^{2}, find the opposite of each term.

$$4p^{2}-4p^{2}+8pq-4q^{2}$$

Combine 4p^{2} and -4p^{2} to get 0.

$$8pq-4q^{2}$$