Expanding brackets, or “multiplying out”, involves multiplying every term inside the bracket by the number or term on the outside with the aim of removing the set of brackets.
The formula for expanding a single bracket is \[a(b+c) = ab + ac\]
The formula for expanding a double bracket is \[(a+b)(c+d) = a(c+d)+b(c+d)=ac + ad + bc + bd\]
This last formula for the product is often referred to as the FOIL method:
$a$ and $c$ are the first terms, $a$ and $d$ are the outside terms, $b$ and $c$ are the inside terms and $b$ and $d$ are the last terms.
Expand $2x(xy-3x^2)$.
Start by multiplying $2x$ by the first term inside the bracket, then by the second. \[2x(xy-3x^2) = 2x \times xy-2x\times 3x^2=2x^2y - 6x^3\]
Expand $(3x-4)(8-2x)$.
Start by multiplying $3x$ by $8$ and $-2x$, then multiply $-4$ by $8$ and $-2x$. \begin{align} (3x-4)(8-2x)&= 3x(8-2x)-4(8-2x)\\ &=24x -6x^2 -32 +8x\\ &=32x -6x^2-32 \end{align}
Prof. Robin Johnson expands the expression $x(2x-1)(2-x)$.
Prof. Robin Johson expands the expression $(x-y)(x+y)$ and talks about the difference of two squares, which comes into use when factorising.
Test yourself: Numbas test on expanding brackets
Test yourself: Numbas test on Algebraic Manipulation