Question

is x+y a factor of x^4 -y^4 ?
please answer this fastly and with correct process​

Answer 1

Answer:

Yes

Step-by-step explanation:

Here are two approaches.  Choose the one you like.

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.

Hope this helps!

Answer 2

Answer:

yes it is a factor of x^4-y^4