Solve 16left(2p-3qright)^2-4left(2p-3qright)

$$16 { \left(2p-3q \right) }^{ 2 } -4 \left( 2p-3q \right)$$

Evaluate

$$4\left(2p-3q\right)\left(8p-12q-1\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2p-3q\right)^{2}.

$$16\left(4p^{2}-12pq+9q^{2}\right)-4\left(2p-3q\right)$$

Use the distributive property to multiply 16 by 4p^{2}-12pq+9q^{2}.

$$64p^{2}-192pq+144q^{2}-4\left(2p-3q\right)$$

Use the distributive property to multiply -4 by 2p-3q.

$$64p^{2}-192pq+144q^{2}-8p+12q$$

Expand

$$64p^{2}-192pq-8p+144q^{2}+12q$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2p-3q\right)^{2}.

$$16\left(4p^{2}-12pq+9q^{2}\right)-4\left(2p-3q\right)$$

Use the distributive property to multiply 16 by 4p^{2}-12pq+9q^{2}.

$$64p^{2}-192pq+144q^{2}-4\left(2p-3q\right)$$

Use the distributive property to multiply -4 by 2p-3q.

$$64p^{2}-192pq+144q^{2}-8p+12q$$