Difference of Two Fourth Powers/Proof 1
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Theorem
- $x^4 - y^4 = \paren {x - y} \paren {x + y} \paren {x^2 + y^2}$
Proof
| \(\ds x^4 - y^4\) | \(=\) | \(\ds \paren {x^2}^2 - \paren {y^2}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {x^2 - y^2} \paren {x^2 + y^2}\) | Difference of Two Squares | |||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {x - y} \paren {x + y} \paren {x^2 + y^2}\) | Difference of Two Squares |
$\blacksquare$