Solve 4(p+q)^2-(2p+q)^2

$$4 ( p + q ) ^ { 2 } - ( 2 p + q ) ^ { 2 }$$

Evaluate

$$q\left(4p+3q\right)$$

Solution Steps

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

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

Use the distributive property to multiply 4 by p^{2}+2pq+q^{2}.

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

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

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

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

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

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

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

Combine 8pq and -4pq to get 4pq.

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

Combine 4q^{2} and -q^{2} to get 3q^{2}.

$$4pq+3q^{2}$$

Expand

$$4pq+3q^{2}$$

Solution Steps

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

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

Use the distributive property to multiply 4 by p^{2}+2pq+q^{2}.

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

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

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

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

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

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

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

Combine 8pq and -4pq to get 4pq.

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

Combine 4q^{2} and -q^{2} to get 3q^{2}.

$$4pq+3q^{2}$$