What is (1+a)^2(1+b^2)-(1+b)^2(1+a^2) ?

The solution to (1+a)^2(1+b^2)-(1+b)^2(1+a^2) is 2a+a^2b^2-b^2a^2+2ab^2-2b-2a^2b

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simplify (1+a)^2(1+b^2)-(1+b)^2(1+a^2)

simplify

(1 + a)^{2} (1 + b^{2}) - (1 + b)^{2} (1 + a^{2})

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

Solution steps

(1 + a)^{2} (1 + b^{2}) - (1 + b)^{2} (1 + a^{2})

Expand

(1 + a)^{2} (1 + b^{2}) : 1 + b^{2} + 2 a + 2 a b^{2} + a^{2} + a^{2} b^{2}

= 1 + b^{2} + 2 a + 2 a b^{2} + a^{2} + a^{2} b^{2} - (1 + b)^{2} (1 + a^{2})

Expand

- (1 + b)^{2} (1 + a^{2}) : - 1 - a^{2} - 2 b - 2 a^{2} b - b^{2} - b^{2} a^{2}

= 1 + b^{2} + 2 a + 2 a b^{2} + a^{2} + a^{2} b^{2} - 1 - a^{2} - 2 b - 2 a^{2} b - b^{2} - b^{2} a^{2}

Group like terms

= 2 a + b^{2} - b^{2} + a^{2} - a^{2} + a^{2} b^{2} - b^{2} a^{2} + 2 a b^{2} - 2 b - 2 a^{2} b + 1 - 1

Add similar elements:

b^{2} - b^{2} = 0

= 2 a + a^{2} - a^{2} + a^{2} b^{2} - b^{2} a^{2} + 2 a b^{2} - 2 b - 2 a^{2} b + 1 - 1

Add similar elements:

a^{2} - a^{2} = 0

= 2 a + a^{2} b^{2} - b^{2} a^{2} + 2 a b^{2} - 2 b - 2 a^{2} b + 1 - 1

Subtract the numbers:

1 - 1 = 0

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

(\frac{1}{2})^{- 2 t}

\frac{5}{x ^{2}} - x - 12 + \frac{3}{x ^{2}} - 16

3 x y + 11 x^{3} y

\frac{( x ^{a + b + 1} \cdot x ^{a - b + 2} )}{( x ^{2 a + 3} )}

4 \cdot (a - b)^{3} - (a - b)

What is (1+a)^2(1+b^2)-(1+b)^2(1+a^2) ?
The solution to (1+a)^2(1+b^2)-(1+b)^2(1+a^2) is 2a+a^2b^2-b^2a^2+2ab^2-2b-2a^2b