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Basic Algebra

 (a + b)2= a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2 a2 – b2 = (a + b)(a – b) a2 + b2 = (a + b)2 – 2ab  or  (a – b)2 + 2ab (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc +ac)  or  a2 + b2 + c2 + 2ab + 2bc + 2ca (a – b – c)2 = a2 + b2 + c2 – 2(ab – bc +ac)  or  a2 + b2 + c2 – 2ab + 2bc – 2ca (a + b)3 = a3 + b3 + 3ab(a + b)  or  a3 + 3a2b + 3ab2 + b3 (a – b)3 = a3 – b3 – 3ab(a – b)  or  a3 – 3a2b + 3ab2 – b3 a3 – b3 = (a – b)(a2 + ab + b2) a3 + b3 = (a + b)(a2 – ab + b2) a4 – b4 = (a2 – b2)(a2 + b2)  or  (a – b)(a + b)(a2 + b2) a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4) an + bn = (a + b)(an-1 – an-2b + an-3b2 … – abn-2 + bn-1)

Indices

 pn = p.p.p…….n times pn⋅ pm = pm+n pn ⋅ qn = (p ⋅ q)n pm/ pn = xm-n pn / qn = (p / q)n (pn)m = pn⋅m pnm = p(nm) p-n = 1 / pn a0 = 1 where a ∈ R , a!=0

Mathematical Properties

 Commutative Property of Addition : a + b = b + a Commutative Property of Multiplication : a x b = b x a Associative Property of Addition : a + (b + c) = (a + b) + c Associative Property of Multiplication : a x (b x c) = (a x b) x c Additive Identity Property : a + 0 = a Multiplicative Identity Property :  a x 1 = a Additive Inverse Property : a + ( – a ) = 0 Multiplicative Inverse Property : a ( 1/a ) = 1 Zero Property of Multiplication  : a x 0 = 0

Mensuration

 Perimeter Square = 4aRectangle = 2a +2bTriangle = a + b + c Circumference Circle = 2 (pi) r = (pi) x diameter Area Square = a2Rectangle = a x bParallelogram = b x hTriangle= ½ (base x height)Trapezoid = h/2 (b1 + b2)Circle = pi x r 2Equilateral Triangle = ½(ah) = [ sqrt(3) / 4 ] x a2Triangle with given a,b,c = sqrt [ s(s-a)(s-b)(s-c) ] when s = (a+b+c)/2 (Heron’s Formula)Sphere = 4 (pi) r2 Surface Area Cube= 6a2Cylinder = 2 . pi . r . hSphere = 4 x pi x r 2 Volume Cylinder = bhCone = bh/3Sphere = 4 x pi x r3 / 3 Pythagoras Theorem a2 + b2 = c2 Distance Formula d = sqrt[(x2 – x1)2 +(y2 – y1)2] Slope of a line m = y2 – y1 / x2 -x1 Mid- Point Formula M = (x1 + x2 )/ 2 , (y1 + y2 )/ 2 Slope-intercept form of the equation of a line y = mx + c Quadratic formula X = [-b ± sqrt(b2 – 4ac)] /2a
*More Formulas will be added very soon… Report any mistake in the comment section.

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### This Post Has 8 Comments

1. NAEEM

THANKS!!! THIS HELPED ALOT

2. ACX

thanks

3. ali

Plzz make one for Physics

4. Nasir

Plz make one for Physics

1. SIKANDAR JAMIL

Amazing!