Question

factorize it please​

Answer 1

Ans---> ( a⁴ + b⁴ ) ( a² - b² )

Given---> ( a⁸ - b⁸ ) / (a² + b² )

To find---> Factorize given expression

Solution---> First we factorize numerator

a⁸ - b⁸ = ( a⁴ )² - ( b⁴ )²

We have an identity,

X² - y² = ( x + y ) ( x - y ) , applying it here we get

a⁸ - b⁸ = ( a⁴ + b⁴ ) ( a⁴ - b⁴ )

= ( a⁴ + b⁴ ) { ( a² )² - ( b² )² }

Applying above identity again, we get

= ( a⁴ + b⁴ ) ( a² + b² ) ( a² - b² )

( a⁸ - b⁸ ) / ( a² + b² )

= (a⁴ + b⁴ ) ( a² + b² ) ( a² - b² ) / ( a² + b² )

( a² + b² ) cancel out from numerator and denominator

= ( a⁴ + b⁴ ) ( a² - b² )