Thread: Express x^8 + 98*(x^4)*(y^4) + y^8 as a product of two polynomials

Express x^8 + 98*(x^4)*(y^4) + y^8 as a product of two polynomials of smaller degree with integer coefficients.

Hint... input at Wolfram|Alpha: Computational Knowledge Engine ... see below

Originally Posted by becz

Express x^8 + 98*(x^4)*(y^4) + y^8 as a product of two polynomials of smaller degree with integer coefficients.

You know from symmetry the LHS has to factor as


Multiplying this out and matching coefficients in the original will give you the factored equation's coefficients. (It took me two pages, but I got there in the end.)

-Dan

You have probably noticed that the expression to be factored has no term. This leads to the conclusion that (using the above factorization proposed by topsquark) a = -d. Similarly, we find that c = -f. This should simplify things, if only slightly.

i get lost when i arrive at 2b = a^2 and 2b = c^2 . i know that a = -c but how can i prove that.

Thanks