Lesson 1: Algebraic Expressions

Property

A term is a constant or the product of a constant and one or more variables. The constant that multiplies the variable(s) in a term is called the coefficient. Like terms are terms that are either constants or have the same variables with the same exponents.

Examples

• In the expression $4x^2 + 7y - 3$, the terms are $4x^2$, $7y$, and $-3$. The coefficient of $4x^2$ is $4$, and the coefficient of $7y$ is $7$.

• Identify like terms in the list: $2a, 5b^2, 6, 9a, 3b^2$. The like terms are $2a$ and $9a$ (both have the variable $a$) and $5b^2$ and $3b^2$ (both have $b^2$).

Property

If $a$, $b$, and $c$ are any numbers, then

If the terms inside parentheses are not like terms, we have no choice but to use the distributive law to simplify the expression.

Examples

• To simplify $5(x+4)$, distribute the 5 to each term: $5(x) + 5(4) = 5x + 20$.
• To simplify $-3(2y-1)$, multiply each inner term by $-3$: $-3(2y) - 3(-1) = -6y + 3$.
• To simplify $(a-5)6$, distribute the 6 from the right: $a(6) - 5(6) = 6a - 30$.

Explanation

The distributive law lets you multiply a number outside parentheses by each term inside. It's like sharing the outside number with every term in the group through multiplication. This is essential when you can't combine the terms inside first.