Solve (a+b)^2-12(a+b)+32

$$( a + b ) ^ { 2 } - 12 ( a + b ) + 32$$

Evaluate

$$\left(a+b-8\right)\left(a+b-4\right)$$

Solution Steps

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

$$a^{2}+2ab+b^{2}-12\left(a+b\right)+32$$

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

$$a^{2}+2ab+b^{2}-12a-12b+32$$

Expand

$$a^{2}+2ab-12a+b^{2}-12b+32$$

Solution Steps

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

$$a^{2}+2ab+b^{2}-12\left(a+b\right)+32$$

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

$$a^{2}+2ab+b^{2}-12a-12b+32$$