Solve (a-b)-b(b-a)]^{2}-2(a-b)^{2}(a+b)^2+a^2(a^2-2b^2)

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

Evaluate

$$\left(a-b\right)\left(b+1\right)$$

Solution Steps

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

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

To find the opposite of b^{2}-ba, find the opposite of each term.

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

The opposite of -ba is ba.

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

Expand

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

Solution Steps

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

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

To find the opposite of b^{2}-ba, find the opposite of each term.

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

The opposite of -ba is ba.

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