Question

$x ^{8} - y ^{8} \div (x - y)$
Answer in factorization ​

Answer 1

STEP1:

y8 Simplify ————— x - y

Equation at the end of step1:

y8 (x8) - ————— x - y

STEP 2 :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole 

Rewrite the whole as a fraction using  (x-y)  as the denominator :

x8 x8 • (x - y) x8 = —— = ———————————— 1 (x - y)

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 2.2       Adding up the two equivalent fractions 

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x8 • (x-y) - (y8) x9 - x8y - y8 ————————————————— = ————————————— 1 • (x-y) 1 • (x - y)

Trying to factor a multi variable polynomial :

 2.3    Factoring    x9 - x8y - y8 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Final result :

x9 + x8y + y8 ————————————— x + y

Answer 2

Answer:

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