Multiplying Polynomial Expressions by Monomials

What are Polynomial Expressions?

Polynomials are regarded as the sums of specific terms of a given form k⋅xⁿ. Here, the k stands for any number and n stands for a positive integer.

How do you Multiply x – y – z by -8x²?

One has to first Multiply each term of the polynomial x – y – z by making use of the monomial -8x².


To multiply x – y – z by -8x², one needs to follow these steps:

  1. Multiply each term of the polynomial by -8x²:
    • -8x² * (x – y – z) = (-8x² * x) – (-8x² * y) – (-8x² * z)
  2. Add the like terms together:
    • -8x³ + 8x²y + 8x²z

Polynomials are algebraic expressions consisting of variables and coefficients, combined using arithmetic operations such as addition, subtraction, multiplication, and division. The general form of a polynomial is represented as k⋅xⁿ, where k is a numerical coefficient and n is a non-negative integer representing the degree of the term.

When multiplying a polynomial by a monomial, each term in the polynomial is multiplied by the monomial separately, and then the resulting terms are combined based on the rules of arithmetic. In the given example of multiplying x – y – z by -8x², the process involves distributing the monomial -8x² to each term of the polynomial and then simplifying the result by adding any like terms.

It is important to pay attention to the signs and coefficients when multiplying polynomials by monomials to ensure the correct computation of the final expression. By following the steps outlined above, one can successfully multiply polynomial expressions by monomials and obtain the desired result.

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