Algebraic Expressions
Lessons in this chapter
About Algebraic Expressions
Algebraic Expressions moves from arithmetic with signed numbers into symbolic algebra, teaching kids to read an expression’s structure before manipulating it.
It opens with identify parts of algebraic expressions and simplify algebraic expressions — naming terms, coefficients, constants, and like terms, then combining like terms (3x + 5x becomes 8x) as the first real algebraic simplification skill.
Add and subtract algebraic expressions extends that combining skill to two full expressions at once, such as (2x + 3) + (5x − 1), reinforcing that only like terms combine and that a subtracted expression needs every one of its terms’ signs flipped first.
Expand algebraic expressions using the distributive property picks up the same distributive-property skill from Integer Operations and applies it to variable expressions, turning something like 3(2x + 4) into 6x + 12 — and mixing in negative coefficients so sign tracking from earlier chapters carries straight through.
Factor algebraic expressions runs the distributive property in reverse, pulling the greatest common factor out of an expression like 6x + 9 to rewrite it as 3(2x + 3) — the skill that later makes solving certain equations and simplifying certain expressions possible without brute-force guessing.
Frequently asked questions
An algebraic expression is a combination of numbers, variables, and operations — like 3x + 5 — with no equal sign and no single fixed value until a number is substituted for the variable. An equation, which this chapter’s own Linear Equations chapter covers next, has an equal sign and makes a claim that two expressions are equal.
A term is a single piece of an expression separated by + or − (like the 3x and the 5 in 3x + 5); the coefficient is the number multiplying a variable (the 3 in 3x); and like terms are terms with the exact same variable raised to the exact same power (3x and 5x are like terms, 3x and 5x² are not).
Add up the coefficients of terms that share the same variable part and leave everything else alone — 3x + 5x becomes 8x, but 3x + 5 stays 3x + 5 because a variable term and a constant can't combine. Identify Parts of Algebraic Expressions and Simplify Algebraic Expressions is where this rule gets introduced before it's used on full expressions.
Forgetting to distribute the subtraction sign across every term of the second expression — (2x + 3) − (5x − 1) is not 2x + 3 − 5x − 1, it's 2x + 3 − 5x + 1, because subtracting an expression flips the sign of every one of its terms, not just the first.
Multiply the number outside the parentheses by every single term inside — 3(2x + 4) means 3 × 2x and 3 × 4, giving 6x + 12, not just 6x + 4. Expand Algebraic Expressions Using the Distributive Property is the exact same skill kids practiced with plain numbers in the Integer Operations chapter, now applied to expressions with a variable.
Dropping or mishandling the sign when the number outside is negative — −2(x − 5) should distribute to −2x + 10 (a negative times a negative gives a positive), but it’s easy to write −2x − 10 by only flipping the first term’s sign and not the second.