Question

algebric solution of a^8+b^8​

Answer 1

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$a^{8}+b^{8}$

$= (-a)^{8}+b^{8}$

$=b^{8}-a^{8}$

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

By using the formula,

x²-y²=(x+y)(x-y)

= (b⁴ + a⁴)(b⁴ - a⁴)

= (b⁴ + a⁴)( (b²)² - (a²)²)

= (b⁴ + a⁴)(b² + a²)(b² - a²)

= (b⁴ + a⁴)(b² + a²)(b + a)(b - a)

-a⁸ + b⁸ = (b⁴ + a⁴)(b² + a²)(b + a)(b - a)

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