Question

Factorize the following algebraic expression :
${x}^{8} - {y}^{8}$
​

Answer 1

x⁸ - y⁸

= (x⁴)² - (y⁴)²

= (x⁴ + y⁴) (x⁴ - y⁴)

= (x⁴ + y⁴) [ (x²)² -( y²)² ]

= (x⁴ + y⁴) [ (x² +y² ) ( x² - y²) ]

= (x⁴ + y⁴) [ (x² +y² ) ( x+y) ( x-y) ]

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Answer 2

Answer:

Hope this helps you......

Step-by-step explanation:

$x {}^{8} - y {}^{8} \\ (x {}^{4} ) {}^{2} - (y {}^{4} ) {}^{2} \\ (x {}^{4} - y {}^{4}) (x {}^{4} + y {}^{4}) \\((x {}^{2}) {}^{2} - (y {}^{2}) {}^{2} ) (x {}^{4} + y {}^{4}) \\ (x {}^{2} + y {}^{2})(x {}^{2} - y {}^{2})(x {}^{4} + y {}^{4}) \\ (x {}^{2} + y {}^{2})(x - y )(x + y)(x {}^{4} + y {}^{4})$