What is (a^2-b^2)/(a+b)-(a+b)^2+2(a^2+ab) ?

The solution to (a^2-b^2)/(a+b)-(a+b)^2+2(a^2+ab) is a^2+a-b^2-b

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simplify (a^2-b^2)/(a+b)-(a+b)^2+2(a^2+ab)

simplify

\frac{a ^{2} - b ^{2}}{a + b} - (a + b)^{2} + 2 (a^{2} + ab)

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

Solution steps

\frac{a ^{2} - b ^{2}}{a + b} - (a + b)^{2} + 2 (a^{2} + ab)

Cancel

\frac{a ^{2} - b ^{2}}{a + b} : a - b

= a - b - (a + b)^{2} + 2 (a^{2} + ab)

Expand

- (a + b)^{2} : - a^{2} - 2 ab - b^{2}

= a - b - a^{2} - 2 ab - b^{2} + 2 (a^{2} + ab)

Expand

2 (a^{2} + ab) : 2 a^{2} + 2 ab

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

Group like terms

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

Add similar elements:

- a^{2} + 2 a^{2} = a^{2}

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

Add similar elements:

- 2 ab + 2 ab = 0

= a^{2} + a - b^{2} - b

x^{2} - 5 x - 5 = 0

4^{2} + 2^{2}

11 x^{3} + 125 x^{2} + 45 x + 11

4 x^{3} - x

\frac{4}{5 - 2 i}

What is (a^2-b^2)/(a+b)-(a+b)^2+2(a^2+ab) ?
The solution to (a^2-b^2)/(a+b)-(a+b)^2+2(a^2+ab) is a^2+a-b^2-b