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Multiplying Monomials – Free Quiz & Examples

  • Multiplying monomials means two multiply two single terms. The single term may have a coefficient and exponents. Multiplying coefficients and then variables gives the complete result.


    A Monomial is a single term having coefficients, variables, or a product of coefficients and variables.

    It can be positive or negative.

    Examples are 5x, 45, x

    Monomials Monomial

    Multiplication of a monomial by monomial

    While doing multiplication you need to follow two steps:

    Step 1: Multiply coefficients

    Multiply the coefficient of the first term by the coefficient of the second term

    Step 2: Multiply exponents

    Multiply variables of the first term with second term variables

    Case 1: If there are similar variables add the power.

    Example: y x y

    Here the power of y is 1 in both cases. Adding power 1 + 1 = 2

    So y x y = y2

    Case 2: If the variables are not alike then do normal multiplication.

    Example: y x z = yz

    Example of multiplication of monomials


                        Example Solution  24 ⋅ 25 24+5
    =29 y4 ⋅ y5 y4+5
    =y9 52 ⋅ y3 25y3
    Note: If you keep the solution same as question here, it works are first term
    do not contain variable and second term lacks coefficient. 3y ⋅ 5y = (3 x 5) ⋅ (y x y)
    = 15y2 3y ⋅ 4z = (3 x 4) ⋅ (y x z)


    Multiplication of monomials


    Multiplying Monomials and a Binomial

    To multiply a monomial by a binomial, simply use the distributive property.

    To do the multiplication of monomial and binomial (two terms) follow two steps:

    Step 1: Multiply monomial with first term

    Multiply the monomial with the first term of the binomial expression.

    Multiplying with the first becomes similar to multiplying two monomials. Now you can just repeat the process above

    Step 2: Multiply monomial with second term

    Multiply the monomial with the second term of the binomial which becomes similar to multiplying monomials.

    Once done check if the result can be further reduced.

    Examples of multiplication of monomial with binomial

    For detail information, free worksheet, free Quizzes, Examples please visit multiplying Monomials