7. Friday, January 25, 2013
ALGEBRAIC
EXPRESSIONS
EXPAND DOUBLE PAIRS OF BRACKETS
HJ. AIRIL AHMAD
AIRIL AHMAD
8. Friday, January 25, 2013
Expand double pairs of brackets
Example 1: Expand (w + v)(x + y)
( w + v ) ( x + y )
= wxx + w x y +vxx + vxy
= wx + wy + vx + vy
AIRIL AHMAD
9. Friday, January 25, 2013
Expand double pairs of brackets
Example 2: Expand (2e + f)(c + d)
( 2e + f ) ( c + d )
= 2e x c + 2e x d +fxc + fxd
= 2ce + 2de + cf + df
AIRIL AHMAD
10. Friday, January 25, 2013
Expand double pairs of brackets
Example 3: Expand (2m + n)(p - s)
( 2m + n ) ( p - s )
= 2m x p + 2m x (-s) + n x p + n x (-s)
= 2mp - 2ms + np - ns
AIRIL AHMAD
11. Friday, January 25, 2013
EXPAND DOUBLE PAIRS OF BRACKETS
HJ. AIRIL AHMAD
AIRIL AHMAD
12. Friday, January 25, 2013
Expand double pairs of brackets
Example 1: Expand (r + 4)(r + 3)
( r + 4 ) ( r + 3 )
= rxr + r x 3 +4xr + 4x3
= r2 + 3r + 4r + 12
= r2 + 7r + 12
AIRIL AHMAD
13. Friday, January 25, 2013
Expand double pairs of brackets
Example 2: Expand (2e + f)(e + 2f)
( 2e + f ) ( e + 2f )
= 2e x e + 2e x 2f +fxe + f x 2f
= 2e2 + 4ef + ef + 2f2
= 2e2 + 5ef + 2f2
AIRIL AHMAD
15. Friday, January 25, 2013
Expand double pairs of brackets
Example 3: Expand (w + 4)(w - 3)
( w + 4 ) ( w - 3 )
= wxw + w x (-3) + 4 x w + 4 x (-3)
= w2 - 3w + 4w - 12
= w2 + w - 12
AIRIL AHMAD
16. Friday, January 25, 2013
EXPAND DOUBLE PAIRS OF BRACKETS
In general , (a+b)2= a2 + 2ab + b2 or
(a-b)2= a2 - 2ab + b2
HJ. AIRIL AHMAD
AIRIL AHMAD
17. Friday, January 25, 2013
Expand same pairs of brackets
Example 1: Expand (r + 4)2
( r + 4 ) ( r + 4 )
= rxr + r x 4 +4xr + 4x4
= r2 + 4r + 4r + 16
= r2 + 8r + 16 AIRIL AHMAD
18. Friday, January 25, 2013
Expand same pairs of brackets
Example 2: Expand (2e + f)2
( 2e + f ) ( 2e + f )
= 2e x 2e + 2e x f + f x 2e + f x f
= 4e2 + 2ef + 2ef + f2
= 4e2 + 4ef + f2 AIRIL AHMAD
19. Friday, January 25, 2013
Expand same pairs of brackets
Example 3: Expand (w - 4)2
( w - 4 ) ( w - 4 )
= w x w+ w x (-4) + (-4) x w + -(4) x (-4)
= w2 - 4w - 4w + 16
= w2 -8w + 16 AIRIL AHMAD
20. Friday, January 25, 2013
State the factors of an algebraic term
Example 1: 2m
1, 2, m, 2m
Example 2: 4g
1, 2, 4, g, 2g, 4g
AIRIL AHMAD
21. Friday, January 25, 2013
State the factors of an algebraic term
Example 3: 12y
1, 2, 3, 4, 6,12, y, 2y, 3y, 4y, 6y, 12y
Example 4: 15k
1, 3, 5, 15, k, 3k, 5k, 15k
AIRIL AHMAD
22. Friday, January 25, 2013
Exercise
Write all the factors of the
following algebraic terms.
5j1. 5n 3. 2
2. 14 p 4. abc
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23. Friday, January 25, 2013
CONCEPT OF
FACTORISATION OF
ALGEBRAIC EXPRESSIONS
AIRIL AHMAD
AIRIL AHMAD
24. Friday, January 25, 2013
Highest Common Factor (HCF)
Find the HCF of the following algebraic terms.
Example 1 : Example 2 :
6h & 4gh 2pq & 4q
2 6h , 4gh 2 2pq , 4q
h 3h , 2gh q pq , 2q
3 , 2g p , 2
HCF = 2 x h HCF = 2 x q
= 2h = 2q
AIRIL AHMAD
25. Friday, January 25, 2013
Highest Common Factor (HCF)
Find the HCF of the following algebraic terms.
Example 3 : Example 4 :
14v2 & 8v 5cd2 & 10cd
2 14v2 , 8v 5 5cd2 , 10cd
v 7v2 , 4v cd cd2 , 2cd
7v , 4 d , 2
HCF = 2 x v HCF = 5 x cd
= 2v = 5cd
AIRIL AHMAD
28. Friday, January 25, 2013
FACTORISE
ALGEBRAIC
EXPRESSIONS
AIRIL AHMAD
AIRIL AHMAD
29. Friday, January 25, 2013
Factorise the following algebraic term
Example 1: 2pq + 4qr
2 2pq + 4qr
q pq + 2qr
(p +
p 2r
2r)
AIRIL AHMAD
30. Friday, January 25, 2013
Factorise the following algebraic term
Example 2: mn – mn2
m mn - mn2
n n - n2
(1 - n
1 n)
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31. Friday, January 25, 2013
Factorise the following algebraic term
Example 3: 3ab + 6bc - 9b2
3 3ab + 6bc - 9b2
b ab + 2bc - 3b2
( a + 2c - 3b3b)
AIRIL AHMAD
33. Friday, January 25, 2013
FACTORISE
ALGEBRAIC
EXPRESSIONS
AIRIL AHMAD
AIRIL AHMAD
34. Friday, January 25, 2013
Factorise ab + ac +bd + cd
Example 9: ag + 3a + 2g + 6
(ag + 3) )+ (2g + 6 )
a
(g 3a a 2
(g 3)2
(a (g + 3) + 2 (g + 3)
)
AIRIL AHMAD
35. Friday, January 25, 2013
Factorise ab + ac +bd + cd
Example 10: mn + 4n + 2m + 8
( mn + 4n) +( 2(m +2 )
(m + 4) n
n 2m 8 4)
(n (m + 4) + 2 (m + 4)
)
AIRIL AHMAD
37. Friday, January 25, 2013
Exercise
Factorise the following algebraic expressions:
1. ac + ad + bc + bd
2. ax + ay + bx + by
3. gh + 2h + 3g + 6
4. a2 + ab + 2a + 2b
5. de + d2 + ef + df
AIRIL AHMAD
38. Friday, January 25, 2013
Factorise a2- b2
Example 11: a 2 – b2
( a 2 – - b2 ) )
(a + b
a
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39. Friday, January 25, 2013
Factorise a2- b2
Example 12: m 2 – n2
((m2 –- n2 ) )
m + n n
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40. Friday, January 25, 2013
Factorise a2- b2
Example 13: 16m2 – 25n2
16m2 – 25n2
( 42m2 – -5n ) )
(4m + 55n
4m n
2 2
AIRIL AHMAD
74. Friday, January 25, 2013
Exercise
Page 139
Ex. 6.3A
No. 1,2,3,5,10,11,12,
13,14,15
AIRIL AHMAD
75. Friday, January 25, 2013
ADD OR SUBTRACT TWO
ALGEBRAIC FRACTIONS WITH
ONE DENOMINATOR AS A
MULTIPLE OF THE OTHER
DENOMINATOR
AIRIL AHMAD
AIRIL AHMAD
76. Friday, January 25, 2013
Simplify the following:
Example 1: 3 xx2 2 x
+
2 x2 4
=6 x+ 2x
4 4
8x
= = 2x
4 AIRIL AHMAD
77. Friday, January 25, 2013
4h x 3 2h
Example 2: +
5 x 3 15
12h +2h
=
15 15
12h + 2h 14h
= =
15 15
AIRIL AHMAD
78. Friday, January 25, 2013
5hx 2 2 h
Example 3: −
6 x 2 12
10h −2h
=
12 12
10h − 2h 8h 2h
= = =
12 12 3
AIRIL AHMAD