Page 45 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

7 3x y ÷ -6x y
2 3
5
m+
m m x a a x x a = a a m+ n n 2 3x y 2 2 3 3 y 3 2 2 y 2
n
m n
n m+
n a =
=
a
a
a
3x
y
= == = 3x 5 y 5 = = y = 3 2x 3
−
6x y
y
−
m m a = m− m− n n − 6x 6x 5 y 2x 2x 3
a
m
a
m−
n
a
a
=
a n a n a n = a 8 3x y ÷ xy
3 2
3x 3x y 3 3 2 2 y 2 2 2
3
m.
n m.
m n
m a ] = a a n m. n n = = y3x== 3x xy y = 3x 3x y 2 y
=
=
a
n =
a [
xy
m ][ ] =
a
xy
[
9 Divide 45a b c by 9a c
2 2
2

m
1/m
1/m m m a 45a 45a b 2 b c 2 c
2
2
2 2
a
1/m = a=
a
a
a
=
= = = = 45a 2 b c
2
9a c
9a 9a 2 c
c
− m − m 1 1
m =
a a = = 1 m =5b 2
−
a
a m a a m
Algebraic Formulae
1 1 = a = m a m
m
1
2
2
2
m
m
a − a − a − m = a 1 (a + b) = a + b + 2ab
2 (a - b) 2 = a + b - 2ab
2
2

m / m / nn m 2 2
n m
n
a
a a m /= n = a n m 3 (a + b) = (a - b) + 4ab
=
a
a
4 (a - b) = (a + b) -4ab ; (a + b)2-(a - b) =4ab
2
2
2
2
3x + 22y 2y 2 2 5 a + b = (a + b) - 2 ab = (a - b)2 + 2 ab
2
2
2y
3x +
2
2
3x +
2
2
2
2
2 +
3y
2x 3y+
2x 2x + 3y 2 2
2
2
_______
_______ 6 a - b = (a + b) (a - b)
_______
2
2
2
5y
x + 2 x + 5y 2 2 7 a + b = (a + b) (a + b - ab)
5y
2
2
2
2
x +
_______
_______
_______
8 a - b = (a - b) (a + b + ab)
3
3
2
2
9 (a + b) = a + b + 3ab (a + b)
3
3
3
12 x 12x y 3 3 2 y = 2 3xy 3xy 10 (a - b) 3 = a - b - 3ab (a - b)
3
2 y
12x
3
3
=
2
2
4x y
4x 4x 2 y = 3xy 11 (a + b + c) 2 = a + b + c + 2 (ab + bc + ca)
y
2
2
2
12 a - b 4 = (a + b ) (a + b) (a - b)
2
2
4
15
15 y 15y 15 y = 10 y 10 Examples
15
10
15y
=
5
15y 15y 5 5 = y 1 If x + y = 9 and xy = 20
15y
2
2
2
2
3a 3a x 2 x 4a x 5a 3 3 Find i) x + y ii) x - y iii) x - y
2
3
x
5a
4a
2 x 5a x 4a
3a
3
3
3
3
4
4
10a
6a 6a 4 x 10a iv) x + y v) x - y vi) x and y
6a 10a x
x
i (a + b) = a + b + 2ab
2
2
2

60a 60a 6 6 (x + y) = x + y + 2xy
6
2
2
2
= = = 60a = 5 a = = a a
5
2
2
60a 60a 5 (9) 2 = x + y + 2 (20)
60a
81 = x + y + 40
2
2
15
25a− − 25a 15 x + y = 81 - 40
15
2
2
= = = − 25a − 8
−
2
−
5a
2
− 5a 5a 8 − 8 x + y = 41
−
ii (a - b) = (a + b) - 4ab
2
2
2
4x 4x y 2 y 2 2
2
4x
2x
2x
= = = 2y 2y = y = 2x 2 (x - y) = (x + y) - 4xy
2
2
=
2y
= (9) - 4 (20)
2
= 81 - 80
32
CITS : WCS - Electrical - Exercise 4