Solve 11(a-b)^2+2(b-a)

$$11 ( a - b ) ^ { 2 } + 2 ( b - a )$$

Evaluate

$$\left(a-b\right)\left(11a-11b-2\right)$$

Solution Steps

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

$$11\left(a^{2}-2ab+b^{2}\right)+2\left(b-a\right)$$

Use the distributive property to multiply 11 by a^{2}-2ab+b^{2}.

$$11a^{2}-22ab+11b^{2}+2\left(b-a\right)$$

Use the distributive property to multiply 2 by b-a.

$$11a^{2}-22ab+11b^{2}+2b-2a$$

Expand

$$11a^{2}-22ab-2a+11b^{2}+2b$$

Solution Steps

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

$$11\left(a^{2}-2ab+b^{2}\right)+2\left(b-a\right)$$

Use the distributive property to multiply 11 by a^{2}-2ab+b^{2}.

$$11a^{2}-22ab+11b^{2}+2\left(b-a\right)$$

Use the distributive property to multiply 2 by b-a.

$$11a^{2}-22ab+11b^{2}+2b-2a$$