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

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

Evaluate

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

Solution Steps

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

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

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

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

Use the distributive property to multiply -4 by p+q.

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

Use the distributive property to multiply -4p-4q by p.

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

Use the distributive property to multiply -4 by p+q.

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

Use the distributive property to multiply -4p-4q by p.

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

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

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

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

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