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anemone
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Factorize $6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)$ as a product of polynomials of lower degree with integer coefficients.
anemone said:Factorize $6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)$ as a product of polynomials of lower degree with integer coefficients.
Factorization is the process of breaking down a mathematical expression into its simplest form by finding its factors. This is often done to simplify the expression and make it easier to work with.
To factorize an expression, you can use a variety of methods such as grouping, difference of squares, or trial and error. In this case, the expression can be factored by using the difference of cubes formula.
The difference of cubes formula is (a^3 - b^3) = (a - b)(a^2 + ab + b^2). It can be used to factorize expressions that have the form of x^3 - y^3.
Yes, the expression can be further simplified by factoring out a common term from each term in the expression. In this case, the common term is (x^2 + y^2 + z^2).
The factors of the given expression are (x^2 + y^2 + z^2) and (6x^3 - 5x^2 + 6y^3 - 5y^2 + 6z^3 - 5z^2).