1. 1.4 Basic Rules of Algebra

2. Terms
terms – parts of an algebraic expression separated by addition (or subtraction) signs
Ex: 2x x (2 times x)
2 terms 2 is the “coefficient” or # part
5 is a “constant” (no variable)

3. Properties commutative property of addition a + b = b + a
Ex: = 3 + 2
commutative property of multiplication
a ∙ b = b ∙ a
Ex: 2 ∙ 3 = 3 ∙ 2
(we can change the order when we add or mult. without changing the result)

4. associative property of addition (a + b) + c = a + (b + c)
Ex: (2 + 3) + 4 = 2 + (3 + 4)
associative property of multiplication
(a ∙ b) ∙ c = a ∙ (b ∙ c)
Ex: (2 ∙ 3) ∙ 4 = 2 ∙ (3 ∙ 4)
6 ∙ 4 = 2 ∙ 12
24 = 24
(we can change the grouping of #s when we add or mult. w/o changing the result)

5. distributive property
I II
3 4
Total Area = Area I + Area II
5(3 + 4) = 5(3) + 5(4)
5(7) =
= 35

6. distributive property a(b + c) = ab + ac a(b – c) = ab – ac Ex: 3(r + 2) = 3(r) + 3(2) = 3r + 6 (2x + 7)4 = 4(2x) + 4(7) = 8x + 28

7. 7(x + y – 2) = 7(x) + 7(y) – 7(2) = 7x + 7y – 14

8. Simplifying an Algebraic Expression
like (or similar) terms – 2 or more terms with the same variables raised to the same powers Ex: terms like terms? 3x, 4x 2a2b, -7a2b ½x2y, 13xy2 5, 8m, 12m

9. Ex: terms like terms? 3x, 4x yes 2a2b, -7a2b yes ½x2y, 13xy2 no 5, 8m, 12m no

10. simplify – reduce the # of terms in an expression
Ex: Simplify by combining like terms
(a) 5x + 2x
= (5 + 2)x
= 7x
(b) 13y – 7y
= (13 – 7)y
= 6y
to combine like terms, just add/sub. the coefficients
If there are ( ), use the distributive property first

11. Ex: Simplify (a) 13a a + 11 = 13a + 2a = 15a + 26 (b) 2(4x + 3) – 5 = 2(4x) + 2(3) – 5 = 8x + 6 – 5 = 8x + 1