Brackets: cheat sheet

Algebra Foundations · The words and methods from the lessons, with an example of each.

expand

Multiply every term inside the bracket by the number outside. Signs come too: $4(3x - 2) = 12x - 8$ .

3(2x + 4) = 6x + 12

change the subject

Undo what was done to the letter, last step first, doing the same to both sides. Check by putting in numbers: $x = 2$ gives $y = 11$ , and $(11 - 5) \div 3 = 2$ .

y = 3x + 5 so x = (y - 5)/3

like terms

Terms with the same letters and powers can be added: $6x - x = 5x$ . Collect them after expanding.

6x + 12 - x = 5x + 12

negative outside

A negative outside flips the sign of every term inside: $-2 \times (-5) = +10$ .

-2(x - 5) = -2x + 10

factorise

Divide every term by the highest common factor and put it outside: $12x - 8 = 4(3x - 2)$ , and $2x^2 + 4x = 2x(x + 2)$ . Check by expanding.

6x + 9 = 3(2x + 3)

6 x-tiles and 9 ones shared into 3 rows of 2x + 3