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Mvaviy Mwyz (Exrmwyzxq Ivwk) : RVB Z N E

This document provides 14 rules and formulas for algebra. It explains how to simplify expressions using properties of exponents, combine like terms, and expand expressions. Examples are provided to demonstrate each rule or formula.

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emdadul2009
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44 views2 pages

Mvaviy Mwyz (Exrmwyzxq Ivwk) : RVB Z N E

This document provides 14 rules and formulas for algebra. It explains how to simplify expressions using properties of exponents, combine like terms, and expand expressions. Examples are provided to demonstrate each rule or formula.

Uploaded by

emdadul2009
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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mvaviY MwYZ

(exRMwYZxq ivwk)
RvbZ ne :
1. + . + = + ; .=+ ; +.= ; .+=
2. (Into ) ev, (.) viv Y cKvk Ki|
3. a
mn
(base GKB nj Yi Power jv hvM nq|)
am
4. a mn (base GKB nj fvMi Power jvi ga weqvM ne|)
an
1
5.
2
1 n
n
6. a (a K cov nq a inversion )
an
7. a a1[base Gi Dci Power bv _vKj 1 aiZ nq|]
8. a 0 1
9. a2 a [ Ges square G KvUvKvwU nq|]
1 1
10. (a 2 ) 2 a 2 [ Kvbv base Gi Dci Power gvb ]
2
1 1 1 1
11. (i ) 1 ; (ii ) 1 ; (iii ) 1 ; (iv ) 1
1 1 1 1
a2 1 a2 1
12. nj ne|
x x x
13. 2a 3a 4b 5b 2 6c 2 nj, ( 2 3 4 5 6) (a a )(b b ) c ne|
2 2

Note : [mvswLK mnMjv GKmv_ Y nq Ges base jv Power mn Y nq|]


ax 6 bx 3 cx 2 2ax
14. GKwU ec`x ivwk|
1 2 3 4
ivwkwUi
(i ) c`msLv 4 wU|
(ii ) x Gi mevP NvZ ev m~PK 6 .
(iii ) x Gi mewbg NvZ 1
15. 2 x 4 110 48 x 36 x 2 8 x 3 ivwkwUK NvZi Aatg (eo-QvU) Abyhvqx mvwRq

cvB,
2 x 4 8 x 3 36 x 2 48 x 100
16. a 6 a a a a a a [base Gi Dci hZ msLK Power _vKe ZZevi base wU Y ne|
hgb : a 3 2 2 2 8
7 1
17. a
a7
18. 2( a b) 2( a ) 2(b)
2a 2b
19. (For Ex 5.1) cqvRbxq m~vejx :

m~ : (a b) 2 a 2 2ab b 2 [mij / Drcv`K wbYq|]


Abywmv : (i ) (a b) 2 (a b) 2 4ab [gvb wbYq|]
(ii ) a b (a b) 2 4ab

Note : a 2 100 nj a 100 10 [ a 2 100 ev, a 100 (eMg~j Ki)]


GKBfve, b 2 36 nj, b 36 6

m~ : (a b) 2 a 2 2ab b 2 [mij / Drcv`K wbYq]


Abywmv : (i ) (a b) 2 (a b) 2 4ab [gvb wbYq|]
(ii ) a b (a b) 2 4ab [gvb wbYq|]

m~ : (a b)(a b) a 2 b 2 [mij / Drcv`K / gvb wbYq|]


Abywmv : (i ) a 2 b 2 (a b) 2 2ab [gvb wbYq|]
(ii ) a 2 b 2 (a b) 2 2ab [gvb wbYq|]

Abywmv : (i ) 4ab (a b) 2 (a b) 2 [gvb wbYq|]


2 2
(ii ) ab a b a b [gvb wbYq|]
2 2

Abywmv : 2(a 2 b 2 ) (a b) 2 (a b) 2 [gvb wbYq|]


m~ : ( x a)( x b) x 2 (a b) x ab [mij / Drcv`K wbYq]
m~ : a 2 b 2 (a b)(a b) [mij / Drcv`K wbYq]
*** m~ : (a b c) 2 a 2 b 2 c 2 2ab 2bc 2ca [mij / Drcv`K / gvb wbYq]
Abywmv : (i ) a 2 b 2 c 2 (a b c) 2 2(ab bc ca) [gvb wbYq|]
(ii ) 2( ab bc ca ) ( a b c ) 2 ( a 2 b 2 c 2 ) [gvb wbYq|]

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