Removing brackets 2
Introduction
In this leaflet we show the correct procedure for writing
expressions of the form ( a + b )( c + d ) in an alternative form
without brackets.
Expressions of the form ( a + b )( c + d ) In the expression (
a + b )( c + d ) it is intended that each term in the first
bracket multiplies each\par term in the second.
( a + b )( c + d ) = ac + bc + ad + bd
Example
Removing the brackets from (5 + a )(2 + b ) gives 5 Ã— 2 + a
Ã— 2 + 5 Ã— b + a Ã— b which simplifies to 10 + 2 a + 5 b + ab
Example
Removing the brackets from ( x + 6)( x + 2) gives x Ã— x + 6
Ã— x + x Ã— 2 + 6 Ã— 2 which equals x + 6 x + 2 x
+ 12 which simplifies to x + 8 x + 12
Example
Removing the brackets from ( x + 7)( x  3) gives x Ã— x + 7
Ã— x + x Ã—3 + 7 Ã— 3 which equals x + 7 x  3 x
 21 which simplifies to
x + 4
x  21
Example
Removing the brackets from (2 x + 3)( x + 4) gives 2 x Ã— x +
3 Ã— x + 2 x Ã— 4 + 3 Ã— 4 which equals 2 x + 3 x + 8 x
+ 12 which simplifies to 2 x + 11 x + 12. Occasionally you will need to
square a bracketed expression. This can lead to errors. Study the
following example.
Example
Remove the brackets from ( x + 1).
Solution
You need to be clear that when a quantity is squared it is
multiplied by itself. So ( x + 1) means ( x +
1)( x + 1). Then removing the brackets gives x Ã— x + 1 Ã— x + x
Ã— 1 + 1 Ã— 1 which equals x + x + x + 1 which simplifies to x + 2 x + 1
Note that ( x + 1) 2 is not equal to x + 1, and
more generally ( x + y ) is not equal to x + y .
Exercises
Remove the brackets from each of the following expressions
simplifying your answers where appropriate.
1. a) ( x + 2)( x + 3), b) ( x  4)( x + 1), c) ( x  1), d) (3 x +
1)(2 x  4).
2. a) (2 x 7)( x  1), b) ( x + 5)(3 x  1), c) (2 x + 1), d)( x  3).
Answers
1. a) x + 5x + 6, b) x  3 x  4, c) x  2 x + 1,
d) 6x10
x  4.\par 2. a) 2 x  9 x + 7, b) 3 x + 14 x 5, c) 4 x + 4 x + 1,
d) x  6
x + 9.
