What is (a^4-b^4)^2+(a^2*b^2)^2 ?

The solution to (a^4-b^4)^2+(a^2*b^2)^2 is a^8+b^8-a^4b^4

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simplify (a^4-b^4)^2+(a^2*b^2)^2

simplify

(a^{4} - b^{4})^{2} + (a^{2} \cdot b^{2})^{2}

a^{8} + b^{8} - a^{4} b^{4}

Solution steps

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

Simplify

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

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

Expand

(a^{4} - b^{4})^{2} : a^{8} - 2 a^{4} b^{4} + b^{8}

= a^{8} - 2 a^{4} b^{4} + b^{8} + a^{4} b^{4}

Group like terms

= a^{8} + b^{8} - 2 a^{4} b^{4} + a^{4} b^{4}

Add similar elements:

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

= a^{8} + b^{8} - a^{4} b^{4}

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- 3 z (z + y) + z^{2}

What is (a^4-b^4)^2+(a^2*b^2)^2 ?
The solution to (a^4-b^4)^2+(a^2*b^2)^2 is a^8+b^8-a^4b^4