Where this sits. This is one of the five algebra families — a little over half the test, and where most students have the least ground under them. Every family page on this site has the same eight parts, in the same order, so once you know the shape of one you know the shape of all of them. Where a part is empty, it says so.
DrillsEighteen drills for this family, one skill each, ten problems at a timeGo to the drills ↓Writing a situation as an expression, and then handling the expression itself: gathering like terms, multiplying out parentheses, adding and subtracting expressions, multiplying two binomials together, and factoring — running the multiplication backward to find what the expression was built from.
An expression is not a question; it is an amount with a variable still in it. Nothing here asks you to find out what the variable is. That comes in the next family — and factoring is the piece to watch, because there it stops being something you do to an expression and becomes the way you solve a quadratic equation.
What the test asks in this family
- How algebra is written — the hidden times sign, and the restThe Thing Called x · Algebra Practice 1
- What a polynomial is, and what is not onePolynomials
- Terms, coefficients, and degreePolynomials
- Gathering like termsPolynomials · Algebra Practice 1
- Signs traveling with their termsPolynomials
- Multiplying a number over parenthesesAlgebra Practice 1 · Quiz 39
- Evaluating an expression: putting a number in for the variableQuiz 33 · Algebra Practice 1
- Writing a situation as an expressionQuiz 33 · Algebra Practice 1
- Adding and subtracting whole polynomialsQuiz 39
- Multiplying two binomials togetherQuiz 39 · Algebra Practice 2
- Factoring — running the multiplication backwardQuiz 39 · Algebra Practice 2
All 11 have something on this site.
Six questions across this family. Nothing here asks you to find out what the variable is — that is the next family. Type an answer and press Check.
- Simplify: 8x + 5 − 3x − 9 5x − 4. Gather like with like: the x terms, 8x − 3x, make 5x; the plain numbers, 5 − 9, make −4. You cannot go further, because 5x and −4 are different kinds of thing. The sign in front of a term travels with it — it is −3x, not 3x.
- Multiply out: 6(2x − 3) 12x − 18. The 6 outside multiplies everything inside, both terms: 6 × 2x = 12x and 6 × −3 = −18. Multiplying only the first term is the usual slip. Think of it as six of those groups added together.
- If x = 4, what is 3x² − 5? 43. Put the number in for the variable, then follow the order of operations: the square comes first, so 4² = 16; then multiply, 3 × 16 = 48; then subtract, 48 − 5 = 43. Doing 3 × 4 first and squaring that gives 139, which is why the order matters here.
- Write this as an expression: five less than twice a number n 2n − 5. Twice the number is 2n, and “five less than” that means five taken away from it. The word order is backwards from the arithmetic, which is exactly the trap: 5 − 2n is a different expression and a wrong answer.
- Multiply out: (x + 4)(x − 2) x² + 2x − 8. Every term in the first binomial multiplies every term in the second: x × x = x², x × −2 = −2x, 4 × x = 4x, 4 × −2 = −8. Then gather: −2x + 4x = 2x.
- Factor: 6x + 15 3(2x + 5). Factoring runs the multiplication backwards: what goes into both 6x and 15? A 3 does. Take it outside and ask what is left of each — 2x and 5. Multiply it back out to check, which is always available to you and always worth doing.
Missed one? Quiz 33: Words to Symbols in Learn it covers writing a situation as an expression and evaluating it. Quiz 39: Out and Back covers adding and subtracting polynomials, multiplying two binomials and factoring. Like With Like under Work it by hand teaches gathering like terms with tiles, and Algebra Practice 1 under On paper has 358 questions on notation, translation and evaluating. Every part of this family now has a lesson.
Want more than these six questions? Flyover I asks about all fourteen families in one sitting and ends in a grid that says where to start; Flyover II asks them again later, with different questions, so you can see what has moved.
- Quiz 33Words to SymbolsWhat a variable is, the words for the four operations, the phrases that run backward, and writing a situation as an expression.
- Quiz 39Out and BackAdding and subtracting whole polynomials, multiplying two binomials, and factoring — running the multiplication backward. The tool family 12 is built on.
Two quizzes and one app, and between them this family is complete. Quiz 33 comes first: it is where a variable starts. Then the app below, if you have not read a polynomial before, and Quiz 39 takes it from there.
Eighteen short drills, one skill each, in order. Each starts with two worked examples, then gives you ten problems (or five) and the reasoning for every answer. Each one prints, with the answer key on the last page. When you get all ten right, or all five right twice in a row, the drill gets a check mark on the Drills page.
- 11.01Words to symbols: phrases into expressions
- 11.02Evaluate an expression with one variable
- 11.03Evaluate with two variables, including negatives
- 11.04Name the terms, coefficients and constants
- 11.05Combine like terms
- 11.06Distribute a number over parentheses
- 11.07Distribute a negative; subtract a group in parentheses
- 11.08Add and subtract polynomials
- 11.09Multiply monomials
- 11.10Multiply a polynomial by a monomial
- 11.11Multiply two binomials
- 11.12Squares of binomials, and the difference of two squares
- 11.13Factor out the greatest common factor
- 11.14Factor x² + bx + c
- 11.15Factor ax² + bx + c
- 11.16Factor a difference of two squares
- 11.17Simplify a fraction with variables by canceling factors
- 11.18Write an expression for a situation
- Polynomials · gathering like with like. Tiles and holes: what a polynomial holds, and how to put the same shapes together. Read this first; Quiz 39 above carries on from where it stops.
- Algebra Practice 2 · 366 problems in three parts: multiplying binomials, factoring, and the two mixed so you have to decide which job a question wants. Every section starts with its plainest version. Answer key at the end. Made to print.
- Algebra Practice 1 · 358 problems on the ground floor of algebra: notation, writing expressions, evaluating, and one-step and two-step equations. Do this one first if the notation is still new.
- Khan Academy, math · free videos and practice. Search it for combining like terms, distributive property, multiplying binomials, factoring. These are the clips we start from in class.
- Math Antics · short, plain videos on the basics.
- Light & Salt Learning · free GED classes online, with playlists by topic.
- Get Sum Math · GED math on video, one topic at a time.
- Kaplan GED Test Prep and the McGraw-Hill Mathematical Reasoning Workbook · look up expressions and polynomials in the contents of either.
On to equations and inequalities, where the variable finally gets pinned down to a number. Everything you did to an expression, you will now do to both sides of an equals sign at once.