Lesson 1: Algebraic Expressions

Property

An algebraic expression consists of numbers and variables connected by arithmetic operations. The numbers are called constants and the letters are called variables. A term is a piece of an expression that is being added or subtracted. This can be either a single number, a single variable, or a product of numbers and variables.

Examples

Property

Algebra tiles are manipulatives that model variables and constants to simplify expressions. Like terms (tiles of the same shape and size) are grouped together. Pairs of opposite tiles (e.g., a positive $x$ and a negative $x$) cancel each other out because their sum is zero, based on the additive inverse property.

Examples

• To simplify $3x + 2 - x + 3$, group the three positive $x$-tiles with the one negative $x$-tile, leaving $2x$. Group the two positive $1$-tiles with the three positive $1$-tiles, giving $5$. The result is $2x + 5$.
• To simplify $4 - 2x + 1 + 3x$, group the negative two $x$-tiles with the three positive $x$-tiles, leaving $x$. Group the four positive $1$-tiles with the one positive $1$-tile, giving $5$. The result is $x+5$.
• To simplify $2y - 1 - 3y + 4$, group the two positive $y$-tiles with the three negative $y$-tiles, leaving $-y$. Group the negative one $1$-tile with the four positive $1$-tiles, giving $3$. The result is $-y + 3$.

Explanation

Simplifying with algebra tiles is like sorting objects. You put all the long $x$-tiles together and all the small $1$-tiles together. If you have a matching positive and negative tile, they form a zero pair and are removed!

Property

To simplify algebraic expressions, apply the laws of algebra by distributing to remove parentheses and combining like terms. This process reduces expressions to their simplest form without changing their value.

Examples