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Multiplying out brackets

When we expand (multiply) two brackets, we need to multiply all the pairs of terms from one bracket and the other.

We want to multiply out the expression $$$(\Tred{x+3})(\Tblue{x-5}).$$$

We muliply all the pairs and add them $$$(\Tred{x+3})(\Tblue{x-5}) = \Tred{x}\times\Tblue{x} + \Tred{3}\times\Tblue{x} + \Tred{x}\times(\Tblue{-5}) +\Tred{3}\times(\Tblue{-5}).$$$

We can then simplify the expression on the right to get $$$(\Tred{x+3})(\Tblue{x-5}) = x^2 + 3x - 5x - 15 = \Tviolet{x^2 -3x -15} $$$

With practice, you can do all the operations in your head.

We give a few additional examples.

\begin{align*} (\Tred{x+1})(\Tblue{x-1})=& x^2 + x - x - 1 = \Tviolet{x^2 - 1}\\ (\Tred{x+1})(\Tblue{y-1})=&\Tviolet{xy + y - x - 1}\\ \Torange{x}(\Tred{x+1})(\Tblue{x-1})=&\Torange{x}(x^2 - 1) = \Tviolet{x^3 - x} \end{align*}