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

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

Evaluate

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

Solution Steps

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

$$a-b-\left(a^{2}-4ab+4b^{2}\right)$$

To find the opposite of a^{2}-4ab+4b^{2}, find the opposite of each term.

$$a-b-a^{2}+4ab-4b^{2}$$

Expand

$$-a^{2}+4ab+a-4b^{2}-b$$

Solution Steps

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

$$a-b-\left(a^{2}-4ab+4b^{2}\right)$$

To find the opposite of a^{2}-4ab+4b^{2}, find the opposite of each term.

$$a-b-a^{2}+4ab-4b^{2}$$