Home/Algebra/Polynomials/Homogeneous polynomial11. PolynomialsHomogeneous polynomialLevel: intermedioIn 11. PolynomialsExampleCopy LaTeXP(x,y)=x2+3xy+2y2P(x,y)=x^2+3xy+2y^2P(x,y)=x2+3xy+2y2Equivalent formCopy LaTeXP(tx1,…,txn)=tdP(x1,…,xn).P(tx_1,\ldots,tx_n)=t^dP(x_1,\ldots,x_n).P(tx1,…,txn)=tdP(x1,…,xn).Tagsalgebraalgebra formulapolynomialsDetailEvery term has the same total degree.Explore the ideaFound an error? Contact us.Related formulasRelatedMultivariable polynomialP(x1,…,xn)=∑αcαx1α1⋯xnαn,P(x_1,\ldots,x_n) = \sum_{\boldsymbol\alpha}c_{\boldsymbol\alpha} x_1^{\alpha_1}\cdots x_n^{\alpha_n},P(x1,…,xn)=α∑cαx1α1⋯xnαn,Open formulaOpen in sectionRelatedMulti-index and total degreex1α1⋯xnαn,x_1^{\alpha_1}\cdots x_n^{\alpha_n},x1α1⋯xnαn,Open formulaOpen in section