Algebra formulas

Quadratic Formula

If ax² + bx + c = 0, then x = (-b + sqrt(b² – 4ac))/2a.

(where a, b, c are constants & a not equal to 0)

Exponents and Radicals

a^xa^y = a^{x + y} a^1/x = _x√a

(a^x)^y = a^xy a^x/y = _y√a^x

(ab)^x = a^xb^x a^x/y = ( _y√a)^x

(a/b)^x = a^x/b^x _x√ab = _x√a _x√b

a^x/a^y = a^x-y _x√(a/b) = _x√a/_x√b

a^-x = 1/a^x _x√_y√a = _xy√a

Absolute Value

|x| < style=""> if and only if -a

|x| > a if and only if either x>a or x<-a

Special Product Formulas

(x + y)(x – y) = x² – y²

(x + y) ² = x² + 2xy + y² (x – y) ² = x² – 2xy + y²

(x + y)³ = x³ + 3xy² + 3xy² + y³ (x – y) ³ = x³ – 3xy² + 3xy² – y³

Binomial Theorem

(x + y)ⁿ = x ⁿ + (ⁿ₁)x ^n-1 y + (ⁿ₂)x ^n-2 y ² + ... + (ⁿ_k)x ^n-k y ^k + ... + y ⁿ,

where (ⁿ_k) = n!/k!(n – k)!

Special Factoring Formulas

X² – y² = (x + y)(x – y)

x² + 2xy + y² = (x + y)² x² – 2xy + y² = (x – y) ²

x³ – y³ = (x – y)(x² + xy + y²) x³ + y³ = (x + y)(x² – xy + y²)

Inequalities

If a>b and b>c, then a>c.

If a>b, then a+c>b+c.

If a>b and c>0, then ac>bc.

If a>b and c<0,>

Exponentials and Logarithms

y = log_ax ó a^y = x log_axy = log_ax + log_ay

log_a (x/y) = log_ax – log_ay log_ax^r = rlog_ax

a^logax = x log_aa^x = x

log_a1 = 0 log_aa = 1

logx = log₁₀x lnx = log_ex

log_bu = log_au/log_ab