Solve 9left(a+bright)^2-16(a+b

$$9 { \left(a+b \right) }^{ 2 } -16(a+b$$

Evaluate

$$\left(a+b\right)\left(9a+9b-16\right)$$

Solution Steps

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

$$9\left(a^{2}+2ab+b^{2}\right)-16\left(a+b\right)$$

Use the distributive property to multiply 9 by a^{2}+2ab+b^{2}.

$$9a^{2}+18ab+9b^{2}-16\left(a+b\right)$$

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

$$9a^{2}+18ab+9b^{2}-16a-16b$$

Expand

$$9a^{2}+18ab-16a+9b^{2}-16b$$

Solution Steps

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

$$9\left(a^{2}+2ab+b^{2}\right)-16\left(a+b\right)$$

Use the distributive property to multiply 9 by a^{2}+2ab+b^{2}.

$$9a^{2}+18ab+9b^{2}-16\left(a+b\right)$$

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

$$9a^{2}+18ab+9b^{2}-16a-16b$$