A problem involving a monomial and a three-term polynomial will involve one polynomial that only has a single term. The second polynomial will have three terms, which will be separated by either a plus sign or a minus sign.


A polynomial problem involving a monomial and a three-term polynomial will look something like: (ay) * (bx^2 + cx + dy)

Example: (2y)(3x^2 + 4x + 5y)

, Rewrite the problem so that all the terms are separate by distributing the single-term polynomial to both terms in the three-term polynomial.


Rewritten, the new equation should look similar to: (ay)(bx^2) + (ay)(cx) + (ay)(dy)

Example: (2y)(3x^2 + 4x + 5y) = (2y)(3x^2) + (2y)(4x) + (2y)(5y)

, The constants refer to the numerical digits in the problem. These are multiplied as they usually would be according to the standard times table.


Again, for this step you are multiplying a, b, c, and d together.
Example: (2y)(3x^2) + (2y)(4x) + (2y)(5y) = 6(y)(x^2) + 8(y)(x) + 10(y)(y)

, The variables refer to the letters in the equation. When you multiply these variables, different variables will simply be combined together. When you multiply a variable by a like variable, though, you raise the power of the variable.


So multiply the the x and y portions of the equation.
Example: 6(y)(x^2) + 8(y)(x) + 10(y)(y) = 6yx^2 + 8xy + 10y^2

, Due to the single-term monomial at the beginning of this equation, you don't need to combine like terms.


When finished, the final answer should be: abyx^2 + acxy + ady^2

Example substituting sample values for constants: 6yx^2 + 8xy + 10y^2
Examine the problem.
Distribute the monomial to all three terms in the polynomial.
Multiply the constants.
Multiply the variables.
Write your final answer.
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