Get some Tricks of Maths Formulas
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
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.
