Algebra - Chennai Tuition Centre,Home tuition in chennai Chennai Tuition Centre

Basic Identies

(a+b) 2 = a 2 + 2ab + b 2

(a-b) 2 = a 2 - 2ab + b 2

a 2 + b 2 = (a+b) 2 - 2ab

a 2 + b 2 = (a-b) 2 + 2ab

a 2 - b 2 = (a+b)(a-b)

(a+b) 3 = a 3 + 3a2b + 3ab2 + b 3

(a-b) 3 = a 3 - 3a2b + 3ab2 - b 3

a 3 + b 3 = (a + b)(a2 - ab + b2)

a 3 - b 3 = (a - b)(a2 + ab + b2)

(a+b)(c+d) = ac + ad + bc + bd

x 2 + (a+b)x + ab = (x + a)(x + b)

Powers

x a x b = x (a + b)

x a y a = (xy) a

(x a) b = x (ab)

x (-a) = 1 / x a

x (a - b) = x a / x b

Logarithms

y = logb(x) if and only if x=b y

logb(1) = 0

logb(b) = 1

logb(x*y) = logb(x) + logb(y)

logb(x/y) = logb(x) - logb(y)

logb(x n) = n logb(x)

logb(x) = logb(c) * logc(x) = logc(x) / logc(b)

Modern Algebra

Closure Property of Addition

Sum (or difference) of 2 real numbers equals a real number

Additive Identity

a + 0 = a

Additive Inverse

a + (-a) = 0

Associative of Addition

(a + b) + c = a + (b + c)

Commutative of Addition

a + b = b + a

Definition of Subtraction

a - b = a + (-b)











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