a² – b² = (a – b)(a + b)

(a+b)² = a² + 2ab + b²

a² + b²= (a – b)² + 2ab

(a – b)² = a² – 2ab + b²

(a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc

(a – b – c)² = a² + b² + c² – 2ab – 2ac + 2bc

(a + b)³ = a³ + 3a²b + 3ab² + b³ 

(a + b)³ = a³ + b³ + 3ab(a + b)

(a – b)³ = a³ – 3a²b + 3ab² – b³

a3 – b3 = (a – b)(a2 + ab + b2)

a3 + b3 = (a + b)(a2 – ab + b2)

(a + b)3 = a3 + 3a2b + 3ab2 + b3

(a – b)3 = a3 – 3a2b + 3ab2 – b3

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)

(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)

a4 – b4 = (a – b)(a + b)(a2 + b2)

a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)


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बीजगणित के कुछ महत्वपूर्ण सूत्र :-

( x + y )² = x² + y² + 2xy

= ( x - y )² + 4xy

( x - y )² = x² + y² - 2xy

= ( x + y )² - 4xy

x² - y² = ( x + y ) ( x - y )

( x + y + z )² = ( x² + y² + z² ) + 2 ( xy + yz + zx )


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बीजगणित के कुछ महत्वपूर्ण सूत्र :-

( x + y )³ = x³ + y³ + 3 xy ( x + y )

( x - y )³ = x³ - y³ - 3 xy ( x - y )

x³ + y³ = ( x + y ) ( x² - xy + y² )

x³ - y³ = ( x - y ) ( x² + xy + y² )

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🔰 Verbs + Prepositions 🔰

A
● accuse sb of
● advise sb on/about sth
● agree with sb about/on sth
● aim at
● apologise to sb for sth
● apply to sb/sth for sth
● approve of
● argue with sb about/for sth
● arrest sb for sth
● arrive at a building
● arrive in a city / town / country
● ask for
● associate with
_______
B
● beg for
● believe in
● belong to
● benefit from
● beware of
● blame sb for sth
● blame sth on sb
● boast about/of
● borrow from
_______
C
● care about sb/sth
● care for sb/sth
● choose from/between
● collaborate with
● combine with
● comment on
● communicate with
● compare with/to
● compete with sb for sth
● complain to sb about/of sth
● concentrate on sth
● confess sth to sb
● congratulate sb on sth
● connect to/with
● consist of
● contrast with
● contribute to
● cooperate with sb
● cope with
● cover sb in/with sth
● criticise for
_______
D
● deal with
● decide on
● dedicate sth to sb
● depart from
● depend on
● describe sth to sb
● differ from
● disagree with sb about/on sth
● disapprove of
● discourage from
● distinguish between
● divide sth between/among
● divide sth into
● divide by (Maths)
● dream about/of
_______
E
● escape from
● exchange sth for sth else
● excuse sb for/from
● experiment on sb/sth with sth
● explain sth to sb
_______
F
● fight with
● fill sth with sth else
● forget about
_______
G
● glance at
_______
H
● head for/towards
● hear about/of sb/sth
● hear from sb
● hope for
_______
I
● include in
● insist on
● introduce sb to sb/sth
● invest in
● invite to
● involve in
_______
J
● join in
_______
K
● know about sth
_______
L
● lean on/against
● lie to sb about sth
● listen to
_______
M
● (be) made of/from
● mean by
● mention to
● mistake sb/sth for sb/sth else
_______
O
● object to sb/sth
● occur to
_______
P
● pay for
● point at/to
● praise sb for sth
● pray for sb/sth
● prefer to
● prepare for
● prevent from
● protect sb from/against sth
● protest about/against/at
● provide sb with sth
● provide sth for sb
● punish sb for
● put the blame for sth on sb
_______
Q
● quarrel with sb about sth
_______
R
● receive sth from sb
● recover from
● reduce sth to
● refer to
● regard sb/sth as
● relate to
● rely on
● remind sb about sth
● remind sb of sb/sth
● replace sth with sth else
● rescue sb from
● result from
● result in
● retire from
_______
S
● save sb from
● sentence sb to
● shout at
● smile at/to
● speak to/with sb
● specialise in
● spend money on sth
● stare at
● steal sth from sb
● succeed in
● suffer from
● supply sb with sth
● suspect sb of
_______
T
● take care of sb/sth
● talk to/with sb about sth
● thank for
● think of/about
● translate from
_______
V
● vote for/against
_______
W
● wait for
● warn sb about/against/of
● waste money on sth
● wonder about
● worry about

@sscexam001

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📚 Daily Current Affairs | 11-07-2021 📚
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Q.1. Who has estimated that India's GDP is going to be 10% in the financial year 2021?
Ans. Fitch Rating

Q.2. Which ministry has been created by the central government to strengthen cooperatives?
Ans. Ministry of Cooperation

Q.3. On the birthday of which American-Serbian inventor, popularly known as the mad scientist, the day is celebrated on July 10?
Ans. Nikola Tesla Day

Q.4. Defense Research and Development Organization and who has started a regular M.Tech program in Defense Technology?
Ans. All India Council for Technical Education

Q.5. From which state of India has the Geographical Indication certified Madrai jasmine flower been exported to America and Dubai?
Ans. Tamil Nadu

Q.6. Indian golfer Udayan Mane has become which Indian golfer to qualify for Tokyo Olympics 2020?
Ans. Second

Q.7. Payment solutions provider Razorpay and which company have jointly launched MandateHQ payment interface?
Ans. Mastercard

Q.8. Scientists of the Central University of which state have discovered a new species of plants in Antarctica?
Ans. Punjab

Q.9. The chief executive officer of the ICC who has been removed from the global body of cricket with immediate effect?
Ans. Manu Sawhney

Q.10. The central government has approved a package of how many crore rupees for the purpose of strengthening the health infrastructure in the country?
Ans. 23,123 Crores

@bankexam001

In which subject are you weak?