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Factor the expression completely.

y^(5)+x^(2)y^(5)
Answer:

Factor the expression completely.\newliney5+x2y5 y^{5}+x^{2} y^{5} \newlineAnswer:

Full solution

Q. Factor the expression completely.\newliney5+x2y5 y^{5}+x^{2} y^{5} \newlineAnswer:
  1. Identify common factors: Identify common factors in both terms.\newlineBoth terms y5y^{5} and x2y5x^{2}y^{5} have a common factor of y5y^{5}.
  2. Factor out common factor: Factor out the common factor from both terms.\newlineWe can factor y5y^{5} out of both terms to get y5(1+x2)y^{5}(1 + x^{2}).
  3. Check for further factorization: Check if the remaining expression inside the parentheses can be factored further.\newlineThe expression 1+x21 + x^{2} cannot be factored further over the real numbers because it is not a difference of squares and has no common factors.
  4. Write final factored form: Write the final factored form.\newlineThe completely factored form of the expression is y5(1+x2)y^{5}(1 + x^{2}).

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