Getting some tricks of Maths

Get some Tricks of Maths Formulas

Hi friends today we have to learning the basic mathematics formulas. Most of the students are scared about the mathematics learning. The basic thing of the maths is formulas, we get remember this formulas to solve an expression easily.

Today we have to learn about this formulas as an topic how to getting some ricks of maths.

Below are the some basic maths formulas for your reference.

 (a + b)2 = a2 + 2ab + b2;

a2 + b2 = (a+b)2 −2ab

 (a − b)2 = a2 − 2ab + b2;

a2 + b2 = (a−b)2 + 2ab

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

 (a + b)3 = a3 + b3 + 3ab(a + b); a3 + b3 = (a+b)3 −3ab(a + b)

 (a − b)3 = a3 − b3 − 3ab(a − b); a3 − b3 = (a−b)3 + 3ab(a − b)

 a2 − b2 = (a+b)(a − b)

 a3 − b3 = (a−b)(a2 + ab + b2)

 a3 + b3 = (a+b)(a2 − ab + b2)

 an − bn = (a−b)(an−1 + an−2b + an−3b2 + _ _ _ +bn−1)

 an = a:a:a : : : n times

am:an = am+n

 n! = (1):(2):(3): : : : :(n−1):n.

 n! = n(n−1)! = n(n − 1)(n − 2)! = : : : : .

 0! = 1.

 (a +b)n = an + nan−1b+ n(n − 1)

2! an−2b2 + n(n − 1)(n − 2)

3! an−3b3 + _ _ _+bn; n > 1.

 a0 = 1 where a 2 R; a 6= 0

 a−n =1an ; an =1a−n

 ap=q = qpap

 If am = an and a 6= _1; a 6= 0 then m=n

 If an = bn where n 6= 0, then a = _b

 Ifpx;py are quadratic surds and if a +px =py, then a = 0 and x = y

 Ifpx;py are quadratic surds and if a+px = b+py then a = b and x = y

 If a;m; n are positive real numbers and a 6= 1, then loga mn = logam+loga n

 If a;m; n are positive real numbers, a 6= 1, then loga_mn_= logam−loga n

 If a and m are positive real numbers, a 6= 1 then logamn = nlogam

 If a; b and k are positive real numbers, b 6= 1; k 6= 1, then logb a =logk alogk b

 logb a =1loga bwhere a; b are positive real numbers, a 6= 1; b 6= 1

 if a;m; n are positive real numbers, a 6= 1 and if logam = logan, thenm=nTypeset by MS-TEX2

 if a + ib = 0 where i =p−1, then a = b = 0

 if a + ib = x + iy, wherei=p−1, then a = x and b = y

 The roots of the quadratic equation ax2+bx+c = 0; a 6= 0 are−b _pb2 − 4ac2aThe solution set of the equation is(−b +p_2a;−b −p_2a)where _ = discriminant = b2 − 4ac

 The roots are real and distinct if _ > 0.

 The roots are real and coincident if _ = 0.

 The roots are non-real if _ < 0.

 If _ and _ are the roots of the equation ax2 + bx + c = 0; a 6= 0 then

i) _ + _ =−ba= − coe_. of xcoe_. of x2

ii) _ _ _ = ca=constant termcoe_. of x2

 The quadratic equation whose roots are _ and _ is (x − _)(x − _) = 0

i.e. x2 − (_ + _)x + __ = 0

i.e. x2 − Sx + P = 0 where S =Sum of the roots and P =Product of the

roots.

Wish you all best luck for your bright future.