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

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

Evaluate

$$b^{2}$$

Solution Steps

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

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

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

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

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

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

Combine a^{2} and -a^{2} to get 0.

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

Combine -2ab and 2ab to get 0.

$$b^{2}$$

Expand

$$b^{2}$$

Solution Steps

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

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

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

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

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

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

Combine a^{2} and -a^{2} to get 0.

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

Combine -2ab and 2ab to get 0.

$$b^{2}$$