Question

Factor x^4+xy^3+x^3+y^3 out completely. Hint: first factor out a monomial.

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Answer 1

Answer:

(x + y)(x^2 - xy + y^2)(x + 1)

Step-by-step explanation:

x(x^4/x + xy^3/x) + (x + y)(x^2 - xy + y^2)

x(x^4-1 + y^3) + (x + y)(x^2 - xy + y^2)

x(x^3 + y^3) + (x + y)(x^2 - xy + y^2)

x(x + y)(x^2 - xy + y^2) + (x + y)(x^2 - xy + y^2)

(x + y)(x^2 - xy + y^2)(x(x + y)(x^2 - xy + y^2/(x + y)(x^2 - xy + y^2 + x(x + y)(x^2 - xy + y^2/x(x + y)(x^2 - xy + y^2)

(x + y)(x^2 - xy + y^2)(x + 1)