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

The solution to (a^2+b^2)^2-(a^2-b^2)^2 is 4a^2b^2

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

simplify

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

4 a^{2} b^{2}

Solution steps

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

Expand

(a^{2} + b^{2})^{2} : a^{4} + 2 a^{2} b^{2} + b^{4}

= a^{4} + 2 a^{2} b^{2} + b^{4} - (a^{2} - b^{2})^{2}

Expand

- (a^{2} - b^{2})^{2} : - a^{4} + 2 a^{2} b^{2} - b^{4}

= a^{4} + 2 a^{2} b^{2} + b^{4} - a^{4} + 2 a^{2} b^{2} - b^{4}

Group like terms

= a^{4} - a^{4} + b^{4} - b^{4} + 2 a^{2} b^{2} + 2 a^{2} b^{2}

Add similar elements:

a^{4} - a^{4} = 0

= b^{4} - b^{4} + 2 a^{2} b^{2} + 2 a^{2} b^{2}

Add similar elements:

b^{4} - b^{4} = 0

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

Add similar elements:

2 a^{2} b^{2} + 2 a^{2} b^{2} = 4 a^{2} b^{2}

= 4 a^{2} b^{2}

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What is (a^2+b^2)^2-(a^2-b^2)^2 ?
The solution to (a^2+b^2)^2-(a^2-b^2)^2 is 4a^2b^2