Solve (p+q+15)(p+q-15)

$$( p + q + 15 ) ( p + q - 15 )$$

Evaluate

$$\left(p+q\right)^{2}-225$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=p+q and b=15.

$$\left(p+q\right)^{2}-15^{2}$$

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

$$p^{2}+2pq+q^{2}-15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$p^{2}+2pq+q^{2}-225$$

Expand

$$p^{2}+2pq+q^{2}-225$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=p+q and b=15.

$$\left(p+q\right)^{2}-15^{2}$$

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

$$p^{2}+2pq+q^{2}-15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$p^{2}+2pq+q^{2}-225$$