Is x+y a factor of x⁴-y⁴

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Is x+y a factor of x⁴-y⁴

Posted by Tarunakumar Dalai 5 years, 4 months ago

CBSE > Class 08 > Mathematics

3 answers

Abhinav Jha 5 years, 3 months ago

yes,x+y a factor ofx⁴-y⁴

1Thank You

Yahiah Rahman 5 years, 4 months ago

Option 1 Since (x-a) is a factor of a polynomial f(x) if f(a) = 0, then (x+y) is factor if f(-y)=0. For f(x) = x⁴-y⁴, this is f(-y) = (-y)⁴ - y⁴ = y⁴-y⁴ = 0. So yes, (x+y) is a factor. Option 2 Factorizing by difference of squares (twice!): x⁴-y⁴ = (x²)² - (y²)² = ( x² - y² ) ( x² + y² ) = ( x - y ) ( x + y ) ( x² + y² ) So yes, (x+y) is a factor.

0Thank You

Yogita Ingle 5 years, 4 months ago

Given x⁴ - y⁴

= ( x² )² - ( y² )²

{ Using identity

a² - b² = ( a + b ) ( a - b ) }

= ( x² + y² ) ( x² - y² )

Again using the identity

= ( x² + y² ) [ ( x )² - ( y )² ]

= ( x² + y² ) ( x + y ) ( x - y )

So, x+y a factor of x⁴-y⁴

0Thank You

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