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

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

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

simplify

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

a^{4} + b^{4}

Solution steps

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

Distribute parentheses

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

Simplify

a^{2} a^{2} + a^{2} b^{2} + a^{2} 2 ab + b^{2} a^{2} + b^{2} b^{2} + b^{2} 2 ab - 2 ab a^{2} - 2 ab b^{2} - 2 ab 2 ab : a^{4} + b^{4} - a^{2} b^{2} + b^{2} a^{2}

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

Add similar elements:

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

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

π \times r \times (9 + r)

- \frac{2 x ( - x ^{2} - 27 )}{( x ^{2} - 9 ) ^{3}}

\frac{n ^{2} \cdot ( n - 1 ) \cdot ( n + 1 )}{12}

(x + 5) (x - 1 + i) (x + 1 + i)

(- \frac{1}{2}) (\frac{1}{2} (1 - x) - \frac{1}{4})

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