MULTIPLYING OUT
The subiect of the
formula is usuallv
wpitten tipst
BRACKETS
• This helps t o simplify algebraic expressions.
• The t e r m outside t h e brackets multiplies each separate t e r m inside t h e brackets.
E X A M P L E S
3 ( 1 7 + 5 ) = 6x + 15
(3 X 2x = 6x, 3 X 5 = 15)
a(3a - 4) =3a' - 4a
b ( 2 a + 3 b - c) = 2 a b + 3 b ' - b e
If t h e t e r m o u t s i d e t h e b r a c k e t is n e g a t i v e , a l l o f t h e s i g n s
of the terms inside the bracket are changed w h e n multiplying out
E X A M P L E S
- 4 5 x ^ 3 ) =-8X - 12
- 2 ( 4 - 3x) =- 8 + 6x
To s i m p l i f y e x p r e s s i o n s e x p a n d t h e brackets first t h e n
collect like terms.
E X A M P L E S
E x p a n d a n d s i m p l i f y 2(x - 3) + x(x + 4).
2(x - 3) + x(x + 4)
= 2x - 6 +X' +4x
Multiply o u t t h e brackets.
= X' + 6x - 6
Collect like terms.
MULTIPLICATION OF
T W O BRACKETS
REARRANGING
FORMUUE
E a c h t e r m in t h e f i r s t b r a c k e t is
multiplied w i t h e a c h t e r m in t h e
second bracket.
T h e s u b i e c t o f a f o r m u l a is t h e l e t t e r t h a t
E a c h t e r m i n t h e f i r s t bpacket i s
multipiied witli tlie second; simpiify
by c o i i e c t i n g Mke t e r m s .
appears o n i t s owin o h o n e side o f t h e f o r m u l a
E X A M P L E S
Make p t h e subject o f these formulae:
a ) r = (p + (6r
b ) 3 ( w + p ) =fcp+ 7
a ) r = (p + (6y
E X A M P L E S
Expand and simplify t h e following.
a ) ( X + 2)(x + 3)
= x ( x + 3) + 2(x + 3)
= x2 + 3x + 2x + 6
= x2 + 5x + 6
b ) (2X + 4)(3X - 2)= 2X(3X - 2) + 4(3X - 2)
= 6x2 - 4 X + 12X - 8
= 6x2 + 8x - 8
c)
= x(x +y) +y(x + y)
= X2 + X y + X y + y2
= X2 + 2Xy + y2
(x
"jommonerporteto
nam
a2 i. HZ
( t h i s is a n i d e n t i t y ;
i t is t r u e f o r all
values of x)
D e a l w i t h t h e power f i r s t .
T a k e t h e st^uare r o o t o f
b o t h sides,
y r = p + 6 Remove ahy t e r m s added o r
subtracted.
So subtract G f r o m both
sides.
V r - 6 =p o r p = V ^ - f e
( b ) 3 ( w + p) = Gp + 7
3 w + 3p =6p + 7
3 w - 7 = 6p - 3p
3 w - 7
= 3p
3 w - 7
W h e n t h e subject
o c c u r s t w i c e , i.e. o n
b o t h sides o f t h e
e<^uais s i g h , t h e y
need t o be collected
o n t o o n e side, as
s h o w n in t h e exarnple.