Factorising and Expanding brackets
How to FACTORISE an equation:
To avoid confusion; x = xx = multiplicationTake the example; 3x +18
In order to factorise we need to find a common factor for both '3x' and '18' and this number will be taken outside the brackets.
For this example the common factor is 3. Because you can divide both '3x' and '18' by 3 to get whole integers.
Now we divide each of the terms ('3x' and '18') by the common factor (3) to give us the numbers in brackets3x ÷ 3 = x18 ÷ 3 = 6
Therefore our factorisation becomes; 3(x + 6)The sign (i.e. + - x or ÷) is the same in brackets as it is in the original equation
How to EXPAND brackets:
Similarly, expanding brackets is the opposite of factorising and so we want to multiply the number/letter that's outside the brackets by EACH of the terms inside the brackets.
So back to the example; 3(x + 6)
To expand the brackets, we multiply 3 by both 'x' and '6'This gets us; 3 x x = 3x3 x 6 = 18
So the expanded version of our factorised equation becomes;3x + 18
Another example of factorising is;y² - 9y
In this example we can divide both terms by 'y' so we put 'y' outside the bracketsy (? ?)
y² ÷ y = y9y ÷ y = 9
Therefore our numbers inside the brackets are 'y' and '9'
y² - 9y = y(y - 9)And another example of expanding brackets is;4x (3y - 4)
We need to multiply 4x by both terms; '3y' and '4'4x x 3y = 12xy4x x 4 = 16x
Therefore; 4x (3y - 4) = 12xy - 16xHave a go at some of these questions if you want some practice;Factorise: 5m + 209 - 3k8x² + 10xyExpand:v(v - 1)6(3 - 4d)p²(3p - 1)
