distributing rules

A. Multiplication

1. addition:  a(b + c) = ab + ac  and  (b + c)a = ba + ca

2. subtraction:  a(b – c) = ab – ac  and  (b – c)a = ba – ca

3. FOIL:  (a + b)(c + d) = ac + ad + bc + bd

Careful!!

a(bc) ≠ ab·ac

B. Division

1. addition:  

2. subtraction:  

Careful!!

C. Exponents   (a ≥ 0, b ≥ 0)

1. multiplication:  (ab)^x = a^xb^x

2. division:       (b ≠ 0)

Careful!!

(a + b)^x ≠ a^x + b^x

(a – b)^x ≠ a^x– b^x

D. Roots   (x ≥ 0, y ≥ 0)

1. multiplication:  

2. division:       ( y ≠ 0)

Careful!!

E. Logarithms   (x > 0, y > 0, a > 0, a ≠ 1)

1. multiplication:  log_a (xy) = log_ax + log_ay

2. division:  

3. powers:  log_a (x^p) = p log_ax

Careful!!

log_a (x + y) ≠ log_ax + log_ay

log_a (x – y) ≠ log_ax– log_ay

F. Trig

1.

2.

3.