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Simplify, expand or factor an expression, one named step at a time.
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The Coddy math course teaches the method itself - you work each step on an interactive board and get told exactly where a move went wrong.
Simplify usually means collect the like terms and finish the arithmetic. Expand means multiply the brackets out even if that makes the expression longer. Factor means the opposite: write it as a product. All three are called simplifying at some point in a school year, and the same expression has a different right answer for each - so this page asks you which one you want rather than guessing.
The steps are the point. Each line says what was done - multiply out, collect like terms, cancel the common factor, reduce the radical - and shows the expression that move produced. Those names are the same ones the Coddy math course uses on its interactive board, because the calculator and the course run on one engine.
Everything stays exact. Three quarters plus five sixths is nineteen twelfths, not 1.5833333; the square root of 12 becomes 2√3 rather than 3.464. A decimal answer is a rounding of the real one, and on a question about fractions or surds a rounding is marked wrong.
Write it the way you would on paper: 2(x - 3) + 4x - 5, x/2 + x/3, sqrt(12), (x^2 - 9)/(x + 3). Use ^ for powers and sqrt(...) for roots.
Simplest form, expanded, or factored. If your homework says "simplify" and you are not sure which is meant, try simplest form first - that is what the word means most of the time.
Each line says which move was made. If you can say why that move came next, you can do the next question without this page.
If your answer differs, the useful question is not which is right but which line diverged. Find that line and the mistake usually explains itself.
The same expression, three ways - and three different right answers depending on what was asked.
| Instruction | Example | Answer |
|---|---|---|
| Simplify | 5x - 2x + 7 | 3x + 7 |
| Simplify (brackets) | 2(x - 3) + 4x - 5 | 6x - 11 |
| Simplify (fractions) | 3/4 + 5/6 | 19/12 |
| Simplify (algebraic fraction) | (x² - 9)/(x + 3) | x - 3 |
| Simplify (radical) | √12 | 2√3 |
| Expand | (x + 2)(x - 3) | x² - x - 6 |
| Expand a square | (2x + 1)² | 4x² + 4x + 1 |
| Factor | x² - 5x + 6 | (x - 2)(x - 3) |
5x - 2x + 75x - 2x is 3x, and the 7 has nothing to combine with, so the answer is 3x + 7. Notice what does NOT happen: the 3x and the 7 do not merge into 10x. Terms with a letter and terms without one are never like terms, and that single confusion accounts for a large share of lost marks in a first algebra course.
2(x - 3) + 4x - 5Multiply out to get 2x - 6 + 4x - 5, then collect: 6x - 11. Doing it the other way round - trying to collect 2(x - 3) with 4x before expanding - is where the classic error of writing 6(x - 3) comes from.
(x^2 - 9)/(x + 3)Factor the top into (x - 3)(x + 3), and now the (x + 3) cancels, leaving x - 3. You may only cancel a whole factor, which is why the factoring has to come first - striking the x² against the x is not a legal move and gives the wrong answer.
3/4 + 5/6The common denominator is 12, so this is 9/12 + 10/12 = 19/12. The answer stays a fraction: 19/12 is exact and 1.5833... is a rounding of it. If the question was about fractions, the fraction is the answer.
