Summarize:

Multiply these as you would any whole numbers. Move the number to the outside of the parentheses. For example, if multiplying (2x3y5)(8xy4){\displaystyle (2x^{3}y^{5})(8xy^{4})}, you would first calculate ((2)x3y5)((8)xy4)=16(x3y5)(xy4){\displaystyle ((2)x^{3}y^{5})((8)xy^{4})=16(x^{3}y^{5})(xy^{4})}. Make sure you are only adding the exponents of terms with the same base (variable). Don’t forget that if a variable shows no exponent, it is understood to have an exponent of 1. For example:16(x3y5)(xy4)=16(x3)y5(x)y4=16(x3+1)y5y4=16(x4)y5y4{\displaystyle 16(x^{3}y^{5})(xy^{4})=16(x^{3})y^{5}(x)y^{4}=16(x^{3+1})y^{5}y^{4}=16(x^{4})y^{5}y^{4}} Take care to add exponents with the same base, and don’t forget that variables with no exponents have an understood exponent of 1. For example: 16(x4)y5y4=16x4y5+4=16x4y9{\displaystyle 16(x^{4})y^{5}y^{4}=16x^{4}y^{5+4}=16x^{4}y^{9}}
Multiply the coefficients. Add the exponents of the first variable. Add the exponents of the remaining variables.