Algebra Formulas
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Important Algebra Formulas
Algebra can be used to solve equations. You will often see equations like 3x+4=5, where you want to find x.
Here is a list of Algebraic formulas –
 a^{2} – b^{2} = (a – b)(a + b)
 (a+b)^{2} = a^{2} + 2ab + b^{2}
 a^{2} + b^{2} = (a – b)^{2} + 2ab
 (a – b)^{2} = a^{2} – 2ab + b^{2}
 (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2ac + 2bc
 (a – b – c)^{2} = a^{2} + b^{2} + c^{2} – 2ab – 2ac + 2bc
 (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3} ; (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)
 (a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}
 a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})
 a^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})
 (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}
 (a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}
 (a + b)^{4} = a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4})
 (a – b)^{4} = a^{4} – 4a^{3}b + 6a^{2}b^{2} – 4ab^{3} + b^{4})
 a^{4} – b^{4} = (a – b)(a + b)(a^{2} + b^{2})
 a^{5} – b^{5} = (a – b)(a^{4} + a^{3}b + a^{2}b^{2} + ab^{3} + b^{4})
 If n is a natural number, a^{n} – b^{n} = (a – b)(a^{n1} + a^{n2}b+…+ b^{n2}a + b^{n1})
 If n is even (n = 2k), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +…+ b^{n2}a – b^{n1})
 If n is odd (n = 2k + 1), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +… b^{n2}a + b^{n1})
 (a + b + c + …)^{2} = a^{2} + b^{2} + c^{2} + … + 2(ab + ac + bc + ….
 Laws of Exponents (a^{m})(a^{n}) = a^{m+n }(ab)^{m} = a^{m}b^{m }(a^{m})^{n} = a^{mn}
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Maths Question Answer
1. If A exceeds B by 40%, B is less than C by 20%, then A C is:
(a) 28 : 25
(b) 26 : 25
(c) 3 : 2
(d) 3 : 1
2. Price of sugar rises by 20%. By how much percent should the consumption of sugar be reduced so that the expenditure does not change?
(a)20
(b)10
(d)15
3. In a school 70% of the students are girls. The number of boys are 510. Then the total number of students in the school is ?
(a) 850
(b) 1700
(c) 1830
(d) 1900
4. Applied to a bill for Rs. 1,00,000 the difference between a discount of 40% and two successive discounts of 36% and 4% is
(a) Nil
(b) Rs. 1,440
(c) Rs. 2,500
(d) Rs. 4,000
5. A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price, how much profit or loss does he make, if any?
(a) 1% gain
(b) 1% loss
(c) 5% gain
(d) No gain, no loss
6. A discount of 15% on one article is the same as discount of 20% on a second article. The costs of the two articles can be
(a) Rs. 85, Rs. 60
(b) Rs. 60, Rs. 40
(c) Rs. 40, Rs. 20
(d) Rs. 80, Rs. 60
7. An agent gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth
(a) Rs. 250
(b) Rs. 500
(c) Rs. 750
(d) Rs. 1,250
8. A sum of money doubles itself at compound interest in 15 years. In how many years it will become eight times?
(a) 30
(b) 45
(c) 50
(d) 60
9. Compound interest (compounded annually) on a certain sum of money for 2 years at 4% per annum is Rs. 102. The simple interest on the same sum for the same rate and for the same period will be
(a) Rs. 99
(b) Rs. 101
(c) Rs. 100
(d) Rs. 98
10. The simplest form of 1.5 : 2.5 is …………… .
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