Expanding brackets

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Expanding basic single brackets

To expand a simple bracket multiply the numbers in the bracket by the number outside the bracket. The basic forumla is:

$$a(b+c)=ab+ac$$

For example:

$$\begin{array}{rl}3(x+2)& =3x+3\cdot 2\\ & =3x+6\end{array}$$

Here are some other examples:

$$\begin{array}{rl}2(4x+5)& =2\cdot 4x+2\cdot 5\\ & =8x+10\\ & \\ 5(2x+3)& =5\cdot 2x+5\cdot 3\\ & =10x+15\end{array}$$

Expanding double brackets

To expand double brackets, its the same process as before but with two brackets. The formula is:

$$\begin{array}{r}(a+b)(c+d)=ac+ad+bc+bd\\ (x+y)(x+z)=x^2+xz+xy+yz\end{array}$$

For example:

$$\begin{array}{rl}(2x+8)(x+4)& =2x\cdot x+2x\cdot 4+8\cdot x+8\cdot 4\\ & =2x^2+8x+8x+32\end{array}$$

Expanding brackets with subtraction

When you have a subtraction in the brackets, you can treat it like a negative number. The formula is:

$$\begin{array}{rl}a(b-c)& =ab-ac\\ 3(x-2)& =3x-3\cdot 2\\ & =3x-6\end{array}$$