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 â€“ b)2 = a2 â€“ 2ab + b2

(a + b) (a â€“ b) = a2 â€“ b2

(x + a)(x + b) = x2 + (a + b)x + ab

(x + a)(x â€“ b) = x2 + (a â€“ b)x â€“ ab

(x â€“ a)(x + b) = x2 + (b â€“ a)x â€“ ab

(x â€“ a)(x â€“ b) = x2 â€“ (a + b)x + ab

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

(a â€“ b)3 = a3 â€“ b3 â€“ 3ab(a â€“ b)

(x + y + z) 2 = x2 + y2 + z2 + 2xy + 2yz + 2xz

(x + y â€“ z) 2 = x2 + y2 + z2 + 2xy â€“ 2yz â€“ 2xz

(x â€“ y + z)2 = x2 + y2 + z2 â€“ 2xy â€“ 2yz + 2xz

(x â€“ y â€“ z)2 = x2 + y2 + z2 â€“ 2xy + 2yz â€“ 2xz

x3 + y3 + z3 â€“ 3xyz = (x + y + z)(x2 + y2 + z2 â€“ xy â€“ yz -xz)

x2 + y2 = 1212 [(x + y)2 + (x â€“ y)2]

(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc

x3 + y3 = (x + y) (x2 â€“ xy + y2)

x3 â€“ y3 = (x â€“ y) (x2 + xy + y2)

x2 + y2 + z2 -xy â€“ yz â€“ zx = 1212 [(x-y)2 + (y-z)2 + (z-x)2]

Powers:

amxan = am+n

aman=amâˆ’naman=amâˆ’n

(am)n = amn

(ambn)p = ampb np

a-m = 1am1am

amn=amâˆ’âˆ’âˆ’âˆšnamn=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 = â€“ âˆ’baâˆ’ba

Quadratic Equation: ax2 + bx + c = 0 x = âˆ’bÂ±b2âˆ’4acâˆš2aâˆ’bÂ±b2âˆ’4ac2a

Discriminant D = b2 â€“ 4ac

Math Formulas:

When rate of discount is given Discount = MPâˆ—Rate of Discount 100

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

Principal = 100âˆ—S.IRâˆ—T100âˆ—S.IRâˆ—T

Rate = 100âˆ—S.IPâˆ—T100âˆ—S.IPâˆ—T

Time = 100âˆ—S.IPâˆ—R100âˆ—S.IPâˆ—R

Principal = Amount â€“ Simple Interest

Discount = MP â€“ SP

Real Number Euclidâ€™s Division Algorithm(lemma) :

Given positive integers `aâ€™ and `bâ€™, there exists unique integers q and r such that a = b.q + r, where 0 â‰¤ 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 â€“ b)2 = a2 â€“ 2ab + b2

(iii) a2 â€“ b2 = (a + b)(a â€“ b)

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

(vii) (a â€“ b)3 = a 3 â€“ b3 â€“ 3ab (a â€“ b )

(viii) a 3 â€“ b3 = (a â€“ b)( a 2 + ab + b2 )

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

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