Solve left(a+bright)^2-12left(a+bright)+36

$${ \left(a+b \right) }^{ 2 } -12 \left( a+b \right) +36$$

Evaluate

$$\left(a+b-6\right)^{2}$$

Solution Steps

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

$$a^{2}+2ab+b^{2}-12\left(a+b\right)+36$$

Use the distributive property to multiply -12 by a+b.

$$a^{2}+2ab+b^{2}-12a-12b+36$$

Expand

$$a^{2}+2ab-12a+b^{2}-12b+36$$

Solution Steps

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

$$a^{2}+2ab+b^{2}-12\left(a+b\right)+36$$

Use the distributive property to multiply -12 by a+b.

$$a^{2}+2ab+b^{2}-12a-12b+36$$