Solve (a-b)^2-14(a-b)+49=

$$( a - b ) ^ { 2 } - 14 ( a - b ) + 49 =$$

Evaluate

$$\left(a-b-7\right)^{2}$$

Solution Steps

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

$$a^{2}-2ab+b^{2}-14\left(a-b\right)+49$$

Use the distributive property to multiply -14 by a-b.

$$a^{2}-2ab+b^{2}-14a+14b+49$$

Expand

$$a^{2}-2ab-14a+b^{2}+14b+49$$

Solution Steps

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

$$a^{2}-2ab+b^{2}-14\left(a-b\right)+49$$

Use the distributive property to multiply -14 by a-b.

$$a^{2}-2ab+b^{2}-14a+14b+49$$