---
title: "Brackets: cheat sheet"
subtitle: "Algebra Foundations"
---

# Brackets

> The words and methods from this unit, with an example of each.

:::keep-together

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

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

_3 rows of 2x + 4: 6 x-tiles and 12 ones_

:::

:::keep-together

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

$$6x + 12 - x = 5x + 12$$

:::

:::keep-together

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

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

:::

:::keep-together

**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_

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:::keep-together

**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 $(11 - 5) \div 3 = 2$.

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

:::