Distributing Rules
Algebra rules for distributing expressions. See factoring rules as well.
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:
C. Exponents (a ≥ 0, b ≥ 0)
1. multiplication: (ab)x = axbx
2. division: (b ≠ 0)
(a + b)x ≠ ax + bx
(a – b)x ≠ ax – bx
D. Roots (x ≥ 0, y ≥ 0)
1. multiplication:
2. division: ( y ≠ 0)
E. Logarithms (x > 0, y > 0, a > 0, a ≠ 1)
1. multiplication: loga (xy) = loga x + loga y
2. division:
3. powers: loga (xp) = p loga x
loga (x + y) ≠ loga x + loga y
loga (x – y) ≠ loga x – loga y
F. Trig
1.
2.
3.
See also
Binomial theorem, fraction rules, exponent rules, radical rules, square root rules, logarithm rules, sum/difference identities