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Closure Property of Addition <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

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)

Closure Property of Multiplication

Product (or quotient if denominator <?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" />0) of 2 reals equals a real number

Multiplicative Identity

a * 1 = a

Multiplicative Inverse

a * (1/a) = 1 (a 0)

(Multiplication times 0)

a * 0 = 0

Associative of Multiplication

(a * b) * c = a * (b * c)

Commutative of Multiplication

a * b = b * a

Distributive Law

a(b + c) = ab + ac

Definition of Division

a / b = a(1/b)

polynomials:

(a+b) ² = a ² + 2ab + b ²

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

a ² - b ² = (a+b)(a-b) (Difference of squares)

a ³ b ³ = (a b)(a ² ab + b ²) (Sum and Difference of Cubes)

x ² + (a+b)x + AB = (x + a)(x + b)

if ax ² + bx + c = 0 then x = ( -b (b ² - 4ac) ) / 2a (Quadratic Formula)

exponents:

Powers

x ^a x ^b = x ^{(a + b)}

x ^a y ^a = (xy) ^a

(x ^a) ^b = x ^(ab)

x ^(a/b) = b^th root of (x ^a) = ( b^th (x) ) ^a

x ^(-a) = 1 / x ^a

x ^{(a - b)} = x ^a / x ^b

Logarithms

y = log_b(x) if and only if x=b ^y

log_b(1) = 0

log_b(b) = 1

log_b(x*y) = log_b(x) + log_b(y)

log_b(x/y) = log_b(x) - log_b(y)

log_b(x ⁿ) = n log_b(x)

log_b(x) = log_b(c) * log_c(x) = log_c(x) / log_c(b)