this is algebra formula everyone can learn from here. if you feel something wrong please lets me know.




Algebra:

(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b) (a – b) = a2 – b2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + a)(x – b) = x2 + (a – b)x – ab
(x – a)(x + b) = x2 + (b – a)x – ab
(x – a)(x – b) = x2 – (a + b)x + ab
(a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – b3 – 3ab(a – b)
(x + y + z) 2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
(x + y – z) 2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
(x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
x2 + y2 = 1212 [(x + y)2 + (x – y)2]
(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
x3 + y3 = (x + y) (x2 – xy + y2)
x3 – y3 = (x – y) (x2 + xy + y2)
x2 + y2 + z2 -xy – yz – zx = 1212 [(x-y)2 + (y-z)2 + (z-x)2]
Powers:

amxan = am+n

aman=am−naman=am−n

(am)n = amn

(ambn)p = ampb np

a-m = 1am1am

amn=am−−−√namn=amn

Rules of Zero:

a1 = a

a0 = 1

a*0 = 0

a is undefined

Linear Equation:

Linear equation in one variable ax + b = 0, x = – −ba−ba

Quadratic Equation: ax2 + bx + c = 0 x = −b±b2−4ac√2a−b±b2−4ac2a

Discriminant D = b2 – 4ac

Math Formulas:

When rate of discount is given Discount = MP∗Rate of Discount 100

Simple Interest = PTR100PTR100 where P = Principal, T = Time in years R = Rate of interest per annum

Principal = 100∗S.IR∗T100∗S.IR∗T

Rate = 100∗S.IP∗T100∗S.IP∗T

Time = 100∗S.IP∗R100∗S.IP∗R

Principal = Amount – Simple Interest

Discount = MP – SP

Real Number Euclid’s Division Algorithm(lemma) :

Given positive integers `a’ and `b’, there exists unique integers q and r such that a = b.q + r, where 0 ≤ r < b ( where a = dividend, b = divisor, q = quotient, and r = remainder. Polynomials In step1 : Factorize the given polynomials, a) Either by splitting the terms, (OR) b) Using these

 

identities :

(i) (a + b)2 = a2 + 2ab + b2

(ii) (a – b)2 = a2 – 2ab + b2

(iii) a2 – b2 = (a + b)(a – b)

(iv) a4 – b4 = (a2 ) 2 – (b2 ) 2 .= (a2 + b2 ) (a2 – b2 ) = (a2 + b2 ) (a – b ) (a + b ) (v) (a + b)3 = a3 + b3 + 3ab (a +b) (vi) a3 + b3 = (a + b)( a 2 + ab + b2 )

(vii) (a – b)3 = a 3 – b3 – 3ab (a – b )

(viii) a 3 – b3 = (a – b)( a 2 + ab + b2 )

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

(x) a 3 + b3 + c3 – 3abc = ( a + b + c )(a2 + b2 + c2 – ab – bc – ac )




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