Solve 4left(a-bright)^2-16left(a-b-1right)

$$4 { \left(a-b \right) }^{ 2 } -16 \left( a-b-1 \right)$$

Evaluate

$$4\left(a-b-2\right)^{2}$$

Solution Steps

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

$$4\left(a^{2}-2ab+b^{2}\right)-16\left(a-b-1\right)$$

Use the distributive property to multiply 4 by a^{2}-2ab+b^{2}.

$$4a^{2}-8ab+4b^{2}-16\left(a-b-1\right)$$

Use the distributive property to multiply -16 by a-b-1.

$$4a^{2}-8ab+4b^{2}-16a+16b+16$$

Expand

$$4a^{2}-8ab-16a+4b^{2}+16b+16$$

Solution Steps

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

$$4\left(a^{2}-2ab+b^{2}\right)-16\left(a-b-1\right)$$

Use the distributive property to multiply 4 by a^{2}-2ab+b^{2}.

$$4a^{2}-8ab+4b^{2}-16\left(a-b-1\right)$$

Use the distributive property to multiply -16 by a-b-1.

$$4a^{2}-8ab+4b^{2}-16a+16b+16$$