Transcript Factorisation (General).

Factorisation.
ab + ad = a( b +……..
Multiplying Out Brackets reminder.
Multiply out the brackets below:
(1) 6 ( x + 3 )
= 6x + 18
(2) 3 ( 2x + 5 ) = 6x + 15
(3) 4 ( 6x + 7 ) =
24x + 28
(4) 9 ( 3x + 9 ) =
27x + 81
(5) 2 ( 3x + 4 ) =
6x + 8
(6) 8 ( 5x + 7 ) =
40x + 56
Putting The Brackets Back In.
In maths it is not only important to be able to multiply
out brackets but also to be able to put the brackets
back. This process is called FACTORISATION.
How to factorise:
Consider the expression below :
6a + 12
= 6 (a + 2 )
Now the
expression is
factorised.
Can you think of a number
that divides into both 6 and
12 ?
6 is a common factor.
Now take 6 outside the bracket
and work out what goes inside
the bracket.
Further Examples.
Now factorise the following expressions:
(1) 5 x + 10 = 5 ( x + 2 )
(2) 7 x + 21 = 7 ( x + 3 )
(3) 6 x - 9 =
3 (2 x - 3 )
(4) 15 x - 20 = 5 ( 3 x - 4 )
(5) 24 x + 8 = 8 ( 3 x + 1 )
What Goes In The Box ?
Factorise the following expressions:
(1) 6x + 12 = 6
(x
+
2)
(2) 9x - 18 =
9
(x
-
2)
(3) 8x + 12 =
4
( 2x
+
3)
(4) 7x - 21 =
7
(x
-
3)
(5) 10x + 15 = 5
( 2x
+
3)
Multiplying Out Brackets Reminder 2
Multiply out the brackets below:
(1) 3t ( 2t + 6 ) = 6t 2 + 18t
(2) 4w ( 3w - 7 ) =12w 2 - 28w
(3) 5a ( 2a + 9 ) = 10a 2 + 45a
(4) 2z ( 5z - 8 ) = 10z 2 - 16z
Harder Factorisation.
In the example below there is more than one term to be
removed from the bracket.
Factorise :
3ab – 12ad
= 3 ( ab – 4 ad )
Remove any numbers first.
= 3a ( b – 4d )
Now remove any letters.
The expression is now fully factorised.
Further Examples.
Factorise the following expressions:
(1) 5wg – 10 wm
(3) 9ab + 12bc
= 5 ( wg – wm )
= 3 ( 3ab + 4bc )
= 5w ( g – m )
= 3b ( 3a + 4c )
(2) 16xy – 8xw
= 8 ( 2xy – xw )
= 8x ( 2y – w )
(4) 6x2 + 9 xy
= 3 ( 2x2 + 3xy )
= 3x ( 2x + 3y )
What Goes In The Box ?
Factorise the following expressions:
(1) 6ag – 18 af
(2) 7x2w + 28xy
=6
( ag
-
3 af )
=7
(x2w
+
4 xy )
= 6a
(g
-
3f)
= 7x ( xw
+
4y )