February 4th
February 4th
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 × 2 + a
× 2 + 5 × b + a × b which simplifies to 10 + 2 a + 5 b + ab
Example
Removing the brackets from ( x + 6)( x + 2) gives x × x + 6
× x + x × 2 + 6 × 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 × x + 7
× x + x ×-3 + 7 × 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 × x +
3 × x + 2 x × 4 + 3 × 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 × x + 1 × x + x
× 1 + 1 × 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) 6x-10
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.
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