- Combine like terms
- operations/operators: In mathematics we call things like multiplication, division, addition, and subtraction operations. They are the verbs of the math world, doing work on numbers and variables. The symbols used to denote operations are called operators, such as [latex]+{, }-{, }\times{, }\div[/latex]. As you learn more math, you will learn more operators.
- term: Examples of terms would be [latex]2x[/latex] and [latex]-\Large\frac{3}{2}[/latex] or [latex]a^3[/latex]. Even lone integers can be a term, like [latex]0[/latex].
- expression: A mathematical expression is one that connects terms with mathematical operators. For example [latex]\Large\frac{1}{2}\normalsize +\left(2^2\right)- 9\div\Large\frac{6}{7}[/latex] is an expression.
Combining Like Terms
One way we can simplify expressions is to combine like terms. Like terms are terms where the variables match exactly (exponents included).
Examples of like terms would be [latex]5xy[/latex] and [latex]-3xy[/latex], or [latex]8a^2b[/latex] and [latex]a^2b[/latex], or [latex]-3[/latex] and [latex]8[/latex].
If we have like terms we are allowed to add (or subtract) the numbers in front of the variables, then keep the variables the same. As we combine like terms we need to interpret subtraction signs as part of the following term. This means if we see a subtraction sign, we treat the following term like a negative term. The sign always stays with the term.
[latex]5x-2y-8x+7y[/latex]
[latex]x^2-3x+9-5x^2+3x-1[/latex]