Expand Brackets, Collect Like Terms and Factor

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Opens on Chapter 8’s example: Roz’s practice booklet: 3(x + 2) + 2(x − 1), tested at x = 7.

Expression (one or two letters) letters, numbers, + − × ÷ ( ) and / for a fraction, ² for a square

Test at an ordinary number, or x = 7, y = 3

Set it equal to (optional) to solve after tidying

Load another example from the book

Enter your numbers, then press Work it out.

How it works

To expand a(b + c), multiply everything inside the bracket by a: 4(x + 3) = 4x + 12, which is the area of a 4 by (x + 3) rectangle, as the picture shows. A minus in front of a bracket changes every sign inside it. Like terms have the same letters to the same powers: 3x and 2x combine, but x² and x don’t. Factoring runs it backward, taking out the biggest number (and letter) every term shares. The table puts one number into every form: if they disagree, a step went wrong. Test with an ordinary number such as 7: a match at 0, 1 or 2 can be luck.

From the book, Chapter 8. 3x + 2x + 7 − x is 4x + 7, and at x = 7 both give 35. 4(x + 3) at x = 5 is 32; 10 − 2(x − 4) at x = 5 is 8; 3s + 2(s + 4) at s = 12 is $68. At x = 2, x² + x is 6 while x³ is 8; at x = 1, (x + 3)² is 16 but x² + 9 is only 10. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. The algebra is done with exact fractions, so 1/3 stays 1/3; decimals are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.