Hg
Name: Class 9 STICK TO YOUR WALL IN STUDY AREA
___________________________________________________________________________________________________________________________________
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The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
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Laws of exponents:
i. (x
a
)
b
= x
ab
Power to the Power, Powers are multiplied.
ii. x
a
x
b
= x
a+b
In multiplication case, same base Powers are added.
iii.
= x
a-b
In division case, same base Powers are subtracted.
iv. x
0
= 1 Anything raised to the power zero is one.
iv. x
a
y
a
= (x y)
a
v.
=
vi. x
-m
=
vii.
=
Algebraic Identities:
I. (a + b)
2
= a
2
+ b
2
+ 2ab
II. (a - b)
2
= a
2
+ b
2
- 2ab
III. (a + b)(a - b) = a
2
- b
2
IV. (a + b)
3
= a
3
+ b
3
+ 3ab(a + b) = a
3
+ b
3
+ 3a
2
b + 3ab
2
V. a
3
+ b
3
= (a + b)(a
2
+ b
2
- ab) [Deduced from Identity IV]
VI. (a - b)
3
= a
3
- b
3
- 3ab(a - b) = = a
3
- b
3
- 3a
2
b + 3ab
2
VII. a
3
- b
3
= (a - b)(a
2
+ b
2
+ ab) [Deduced from Identify VI]
VIII. (a + b + c)
2
= a
2
+ b
2
+ c
2
+ 2ab + 2bc + 2ca
IX. a
3
+ b
3
+ c
3
- 3abc = (a + b + c)(a
2
+ b
2
+ c
2
- ab - bc - ca)
If (a + b + c) = 0, then a
3
+ b
3
+ c
3
= 3abc
X. (x + a)(x + b) = x
2
+ (a + b)x + ab [If b=a, then this becomes identity I, verify!!]
XI. a
2
+ b
2
= (a + b)
2
– 2ab = (a-b)
2
+ 2ab
