Solve 12(p+q)^2-16(p+q)

$$12 ( p + q ) ^ { 2 } - 16 ( p + q )$$

Evaluate

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

Solution Steps

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

$$12\left(p^{2}+2pq+q^{2}\right)-16\left(p+q\right)$$

Use the distributive property to multiply 12 by p^{2}+2pq+q^{2}.

$$12p^{2}+24pq+12q^{2}-16\left(p+q\right)$$

Use the distributive property to multiply -16 by p+q.

$$12p^{2}+24pq+12q^{2}-16p-16q$$

Expand

$$12p^{2}+24pq-16p+12q^{2}-16q$$

Solution Steps

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

$$12\left(p^{2}+2pq+q^{2}\right)-16\left(p+q\right)$$

Use the distributive property to multiply 12 by p^{2}+2pq+q^{2}.

$$12p^{2}+24pq+12q^{2}-16\left(p+q\right)$$

Use the distributive property to multiply -16 by p+q.

$$12p^{2}+24pq+12q^{2}-16p-16q$$