Download 1.4 Basic Rules of Algebra

1.4 Basic Rules of Algebra
Terms
terms – parts of an algebraic expression
separated by addition (or subtraction) signs
Ex: 2x + 5
2 terms
2x (2 times x)
2 is the “coefficient” or # part
5 is a “constant” (no variable)
Properties
commutative property of addition
a+b=b+a
Ex: 2 + 3 = 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)
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)
distributive property
5
I
II
3
4
Total Area = Area I + Area II
5(3 + 4) = 5(3) + 5(4)
5(7)
= 15 + 20
35
= 35
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(x + y – 2)
= 7(x) + 7(y) – 7(2)
= 7x + 7y – 14
Simplifying an Algebraic Expression
like (or similar) terms – 2 or more terms with the
same variables raised to the same powers
Ex:
terms
3x, 4x
2a2b, -7a2b
½x2y, 13xy2
5, 8m, 12m
like terms?
Ex:
terms
3x, 4x
2a2b, -7a2b
½x2y, 13xy2
5, 8m, 12m
like terms?
yes
yes
no
no
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
Ex: Simplify
(a) 13a + 15 + 2a + 11
= 13a + 2a + 15 + 11
= 15a + 26
(b) 2(4x + 3) – 5
= 2(4x) + 2(3) – 5
= 8x + 6 – 5
= 8x + 1