Solve 2(p-1)^2-4q(p-1)

$$2 ( p - 1 ) ^ { 2 } - 4 q ( p - 1 )$$

Evaluate

$$2\left(p-1\right)\left(p-2q-1\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(p-1\right)^{2}.

$$2\left(p^{2}-2p+1\right)-4q\left(p-1\right)$$

Use the distributive property to multiply 2 by p^{2}-2p+1.

$$2p^{2}-4p+2-4q\left(p-1\right)$$

Use the distributive property to multiply -4q by p-1.

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

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(p-1\right)^{2}.

$$2\left(p^{2}-2p+1\right)-4q\left(p-1\right)$$

Use the distributive property to multiply 2 by p^{2}-2p+1.

$$2p^{2}-4p+2-4q\left(p-1\right)$$

Use the distributive property to multiply -4q by p-1.

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