Solve ((n-b)-(a-b)(a-b)

$$( ( n - b ) - ( a - b ) ( a - b )$$

Evaluate

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

Solution Steps

Multiply a-b and a-b to get \left(a-b\right)^{2}.

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

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

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

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

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

The opposite of -2ab is 2ab.

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

Expand

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

Solution Steps

Multiply a-b and a-b to get \left(a-b\right)^{2}.

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

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

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

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

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

The opposite of -2ab is 2ab.

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