$ 2(3x - 4) = \phantom{.} $ $ 6x - 8 $

Solutions

$2$ is multiplied by the expression $3x - 4$, thus every term inside the bracket must be multiplied:

$ 18x - \frac{1}{2}[4x - 2(3 - x)] = \phantom{.} $ $ 15x + 3 $

Solutions

Always expand the inner bracket first:

$ (1 + 2x)(3x - 4) = \phantom{.} $ $ 6x^2 - 5x - 4 $

Solutions

This means the expression $(1 + 2x)$ is multiplied by the expression $(3x - 4)$:

Common mistake #1

$ 1 + 2x(3x - 4) = \phantom{.} $ $ 1 + 6x^2 - 8x $

Solutions

Only the term $2x$ is multiplied by the expression $(3x - 4)$:

Common mistake #2

$ (1 + 2x) - (3x - 4) = \phantom{.} $ $ 5 - x $

Solutions

Subtracting the bracket means the signs inside the second bracket change:

$ (a + b)^2 = \phantom{.} $ $ a^2 + 2ab + b^2 $

Example

$ (6x + 7y)^2 = \phantom{.} $ $ 36x^2 + 84xy + 49y^2 $

Solutions

$ (a - b)^2 = \phantom{.} $ $ a^2 - 2ab + b^2 $

Example

$ (1 - 2xy)^2 = \phantom{.} $ $ 1 - 4xy + 4x^2 y^2$

Solutions

$ (a + b)(a - b) = \phantom{.} $ $ a^2 - b^2 $

Example

$ \left( \frac{1}{2}y + 3y\right)\left( \frac{1}{2}y - 3y\right) = \phantom{.} $ $ \frac{1}{4}y^2 - 9x^2 $

Solutions