How to factor x^5-y^5?

ystyrixkzd

ystyrixkzd

Answered question

2023-03-16

How to factor x 5 y 5 ?

Answer & Explanation

2b1jbp50

2b1jbp50

Beginner2023-03-17Added 2 answers

Factorize using the algebraic identity:
The given expression is x 5 y 5 .
According to the algebraic identity,
a n b n = ( a b ) ( a n 1 + a n 2 b + . . . + a b n 2 + b n 1 )
Then, the given expression can be factorized as follows,
x 5 y 5 = ( x y ) ( x 5 1 + x 5 2 y + x 5 3 y 2 + x 5 4 y 3 + x 5 5 y 4 ) x 5 y 5 = ( x y ) ( x 4 + x 3 y + x 2 y 2 + x 1 y 3 + x 0 y 4 ) x 5 y 5 = ( x y ) ( x 4 + x 3 y + x 2 y 2 + x y 3 + 1 × y 4 ) [ a 0 = 1 ] x 5 y 5 = ( x y ) ( x 4 + x 3 y + x 2 y 2 + x y 3 + y 4 )
Hence, the factors of x 5 y 5 obtained by using the algebraic identity is ( x y ) ( x 4 + x 3 y + x 2 y 2 + x y 3 + y 4 )

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