Factor (x+y)^7−(x^7+y^7)

Kevin Charles

Kevin Charles

Answered question

2022-10-12

Factor ( x + y ) 7 ( x 7 + y 7 )

Answer & Explanation

spornya1

spornya1

Beginner2022-10-13Added 18 answers

Expand ( x + y ) 7 , you would get:
( x + y ) 7 ( x 7 + y 7 ) = x 7 + 7 x 6 y + 21 x 5 y 2 + 35 x 4 y 3 + 35 x 3 y 4 + 21 x 2 y 5 + 7 x y 6 + y 7 x 7 y 7 = 7 x 6 y + 21 x 5 y 2 + 35 x 4 y 3 + 35 x 3 y 4 + 21 x 2 y 5 + 7 x y 6 = 7 x y ( x 5 + 3 x 4 y + 5 x 3 y 2 + 5 x 2 y 3 + 3 x y 4 + y 5 ) = 7 x y ( x + y ) ( x 4 + 2 x 3 y + 3 x 2 y 2 + 2 x 3 + y 4 ) = 7 x y ( x + y ) ( x 2 + x y + y 2 ) 2 , which is your given answer.

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