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INDIAN_ARMY19890

polynomial

(a+b)² = a² + 2ab + b²

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

a² - b² = (a+b)(a-b) (Difference of squares)

a³ b³ = (a b)(a² ab + b²) (Sum and Difference of Cubes)

x² + (a+b)x + AB = (x + a)(x + b)

if ax² + bx + c = 0 then x = ( -b (b² - 4ac) ) / 2a (Quadratic Formula)

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

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(xⁿ) = n log_b(x)

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

Conic Sections	Point x^{^2} + y^{^2} = 0	Circle x^{^2} + y^{^2} = r^{^2}
Ellipse x^{^2} / a^{^2} + y^{^2} / b^{^2} = 1	Ellipse x^{^2} / b^{^2} + y^{^2} / a^{^2} = 1	Hyperbola x^{^2} / a^{^2} - y^{^2} / b^{^2} = 1
Parabola 4px = y^{^2}	Parabola 4py = x^{^2}	Hyperbola y^{^2} / a^{^2} - x^{^2} / b^{^2} = 1
For any of the above with a center at (j, k) instead of (0,0), replace each x term with (x-j) and each y term with (y-k) to get the desired equation.