How do you simplify and divide #(x^3+y^3)div(x+y)#? Precalculus Real Zeros of Polynomials Long Division of Polynomials 1 Answer Narad T. Dec 12, 2016 The answer is #=x^2-xy+y^2# Explanation: We know that #a^3+b^3=(a+b)(a^2-ab+b^2)# So, #(x^3+y^3)=(x+y)(x^2-xy+y^2)# Therefore, #(x^3+y^3)/(x+y)=(cancel(x+y)(x^2-xy+y^2))/cancel(x+y)# #=x^2-xy+y^2# Answer link Related questions What is long division of polynomials? How do I find a quotient using long division of polynomials? What are some examples of long division with polynomials? How do I divide polynomials by using long division? How do I use long division to simplify #(2x^3+4x^2-5)/(x+3)#? How do I use long division to simplify #(x^3-4x^2+2x+5)/(x-2)#? How do I use long division to simplify #(2x^3-4x+7x^2+7)/(x^2+2x-1)#? How do I use long division to simplify #(4x^3-2x^2-3)/(2x^2-1)#? How do I use long division to simplify #(3x^3+4x+11)/(x^2-3x+2)#? How do I use long division to simplify #(12x^3-11x^2+9x+18)/(4x+3)#? See all questions in Long Division of Polynomials Impact of this question 18546 views around the world You can reuse this answer Creative Commons License