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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:  

Careful!!

 

C. Exponents   (a ≥ 0, b ≥ 0)

1. multiplication:  (ab)x = axbx

2. division:       (b ≠ 0)

Careful!!

(a + b)xax + bx

(ab)xax – bx

 

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:  loga (xy) = loga x + loga y

2. division:  

3. powers:  loga (xp) = p loga x

Careful!!

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

 


  this page updated 21-feb-16
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes