Expressions

Expressions

Hi, this is Wyatt, and today we're going to be talking about expressions.

We're going to learn about monomials, binomials, trinomials, and expressions with more than three terms. We'll also learn how to write expressions in standard form.

Types of Expressions

A monomial has one term.

5x²

A binomial has two terms.

3x + 2

A trinomial has three terms.

x² + 4x + 7

If an expression has more than three terms, it is not a monomial, binomial, or trinomial.

Standard Form

To write an expression in standard form, arrange the terms from the greatest exponent to the smallest exponent. The constant term should be written at the end.

Example 1

Write the following expression in standard form:

4m⁴n − 4 + 9mn + 1⅜m³n

First, find the term with the greatest exponent.

4m⁴n

Next comes the term with the next greatest exponent:

1⅜m³n

Then:

9mn

Finally, place the constant at the end:

-4

Standard Form: 4m⁴n + 1⅜m³n + 9mn − 4

Example 2

Write the following expression in standard form:

n⁵ − ½m⁴ + 3m²n³ + 15

The greatest exponent is 5, so:

n⁵

Next is:

−½m⁴

Then:

3m²n³

Finally, the constant:

+15

Standard Form: n⁵ − ½m⁴ + 3m²n³ + 15

Example 3: Classifying Expressions

Label each expression as:

  • M = Monomial
  • B = Binomial
  • T = Trinomial
  • N = None of these

    • Expression 1

    This expression has two terms.

    Two terms means it is a binomial.

    Answer: B

    Expression 2

    This expression has three terms.

    Three terms means it is a trinomial.

    Answer: T

    Expression 3

    This expression has one term.

    One term means it is a monomial.

    Answer: M

    Conclusion

    Today we learned:

  • What monomials, binomials, and trinomials are
  • How to identify the number of terms in an expression
  • How to write expressions in standard form
  • How to classify expressions

    • These are important skills you'll use throughout Algebra.

    Thanks for watching, and bye for now!