Skip to main content

Algebra Important formula and identities

 Algebra

Important formula and identities



i. (a+b)² = a²+2ab+b² = (a-b)²+4ab

ii. (a-b)² = a²-2ab+b² = (a+b)²-4ab

iii. a²+b² = (a+b)²-2ab = (a-b)²+2ab

iv. a²-b² = (a+b)(a-b)

v. (a-b)³ = a³-b³-3a²b+3ab² = a³-b³-3ab(a-b)

vi. a³+b³ = (a+b)³-3ab(a+b) = (a+b)(a²-ab+b²)

vii. a³-b³ = (a-b)³+3ab(a-b) = (a-b)(a²+ab+b²)

viii. a³+b³+c³-3abc = 1/2(a+b+c)[(a-b)²+(b-c)²+(c-a)²]

ix. a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)

x. (a+b)³ = a³+b³+3a²b+3ab² = a³+b³+3ab(a+b)

xi. a⁴-b⁴=(a²+b²)(a+b)(a-b)

xii. (a+b+c)² = a²+b²+c²+2ab+2bc+2ca

xiii. (a-b+c)² = a²+b²+c²-2ab-2bc+2ca

xiv. (a+b-c)² = a²+b²+c²+2ab-2bc-2ca

xv.  (a-b-c)² = a²+b²+c²-2ab+2bc-2ca

xvi. (x-a)(x+b) = x²+(a+b)x+ab

xvii. (x-a)(x-b) = x²-(a+b)x+ab

xviii. a²(b+c)+b²(c-a)+c²(a+b)+2abc = (a+b)(b+c)(c+a)

xix.  a²(b²-c²)-b²(c²-a²)+c²(a²-b²) = (a-b)(b-c)(c-a)

xx. ab(a-b)+bc(b-c)+ca(c-a) = -(a-b)(b-c)(c-a)

xi. (a+b)²+(a-b)²=2(a²+b²)

xii. (a+b)²-(a-b)² = 4ab

xiii. (a+b+c)³ = a³+b³+c³+3(a+b)(b+c)(c+a)

xiv. 2a²b²+2b²c²+2c²a²-a⁴-b⁴-c⁴ = (a+b+c)(a-b+c)(b+c-a)(a+b-c)


xv. (a+b+c)³-a³-b³-c³ = 3(a+b)(b+c)(c+a)




Maths formula for jee aspirant

physics formula for jee aspirant

Top Engineering colleges list

Labels:

Comments

Post a Comment

Thanks for your comments

Read this Article

Poverty as a Challenge ncert notes

 Chapter-3 Economics  Poverty as a Challenge  In our daily life we come across many poor people such as landless labourers in villages, people living in jhuggis, daily wage workers at construction sites, child labourers in dhabas, rickshaw-pullers, domestic servants, cobblers, beggars, etc. • Poverty : Usually the levels of income and consumption are used to define poverty. In India, poverty has been defined as a situation in which a person fails to earn income sufficient to buy him bare means of subsistence.  • Other Indicators of Poverty : Now poverty is looked through other indicators like illiteracy level, lack of access to health care, lack of job opportunities, lack of access to safe drinking water, sanitation, etc. Nowadays, the concept of social exclusion is becoming very common in the analysis of poverty.  • Estimates of Poverty : The incidence of poverty in India was around 55 per cent in 1973 which declined to 36 per cent in 1993 and further to 26 per cent in 200
Post a Comment
Next ⏭️

The Story of Village Palampur-key points - digieducation learning point

  Chapter – 1 Economics  The Story of Village Palampur - key points  • Village Palampur: Palampur is a small village having about 450 families. It is 3 km away from Raiganj — a big village. Shahpur is the nearest town to the village.  • Main Production Activities: Farming is the main production activity in the village Palampur.  Most of the people are dependent on farming for their livelihood. Non-farming activities such as dairy, small-scale manufacturing (e.g. activities of weavers and potters, etc.), transport, etc., are carried out on a limited scale. • Factors of Production (Or Requirements for Production of Goods and Services): Land, labour and capital are the basic requirements for production of goods and services which are popularly known as factors of production. Land includes all free gifts of nature, e.g., soil, water, forests, minerals, etc. Labour means human effort which of course includes physical as well as mental labour. Physical capital is the third requir
Post a Comment
Next ⏭️

Lists of IIITs in India for students

  List of IlITs Lists of IIITs in India 1. Atal Bihari Vajpayee lIT, Gwalior, MP 2. IIIT, Kanchipuram, Tamil Nadu 3. IIIT, Kottayam, Kerala 4. IIIT, Jhalwa, Allahabad, Uttar Pradesh 5. Pandit Dwarka Pd. Mishra lIIT, Jabalpur, M.P. 6.IIIT, Guwahati, Assam 7. IIIT, Kota, Rajasthan 8. IIIT, Chittoor, Andhra Pradesh 9. IIT, Vadodara, Gujarat 10. IIIT, Una, Himachal Pradesh 11. IIIT, Kalyani, West Bengal 12. IIIT, Sonepat, Haryana 13. IIIT, Tiruchirapalli 14. IIIT, Lucknow 15. IIIT, Manipur Mantripukhri, Imphal 16.Indian Institute of Information Tech., Dharwad 17. Indian Institute of Information Tech., Ranchi 18. IIIT, Kurnool, Andhra Pradesh 19. Indian Institute of Information Tech., Nagpur 20. Indian Institute of Information Tech., Pune 21. Indian Institute of Info. Tech., Bhagalpur 22. Indian Institute of Information Tech., Bhopal 23. Indian Institute of Information Tech., Surat 24. Indian Institute of Information Tech., Agartala 25.Indian Institute of Information Tech., Karnataka 26.
Post a Comment
Next ⏭️