Download Variable Expressions

Variable Expressions
Variable is any letter of the alphabet.
Example: a, b, c, d, ..., x, y,(xy)z, etc... .
An expression that contains one or more variables is called variable expression.
Example:
2xy - Sx2 + ly + 4x - 9 is a variable expression
Numerical Coefficients
Variable terms
CM-fkutui- L
x
X^JcjnlpO
LfX
-9 Constant term
Evaluate variable expressions
Exercise 1: Evaluate the variable expression when a = 4, b = -6, c = -4, and d = -8
a) 10a-8b = lO (/*) - g(-&) = ^0-(-U5)= L,0 +4#=£<?
•'
b)t=-
^
c) a&-62 = q^ _ (_.u^ _ 4(_-l/) _30>
2
d)
o2-ft2
a-6
i
k-3G
^+6
2 vg
-
~Z
Properties of Numbers:
1. Commutative Property of Addition
a + b = b + a
Example: 3 + 7 = 7 + 3
2.J Commutative Property of Multiplication
VV
ab = ba
Example: 3x7 = 7x3
3. Associative Property of Addition
a + (b + c) = (ci + b) + c
Example: 3 + (7 + 2) = (3 + 7) + 2
I*
12-
4. Associative Property of Multiplication
^y
a(bc) = (ab)c
Example: 3(7 x 2) = (3 x 7) x 2
„ .^
if*.
^~^( 5. Addition Property of Zero
a+0=0+a=a
Example: 3 + 0 = 0 + 3 = 3
[6.J Multiplication Property of Zero
ax0=0xa=0
Example: 3x0 = 0x3 = 0
7. Multiplication Property of One
axl=lxa=a
Example: 3x1 = 1x3 = 3
8. Inverse Property of Addition
a + (-a) = (-a) + a = 0
Examples + (-3) = (-3) + 3 = 0
9. Inverse Property of Multiplication
Example:3 x- = -x3 = l
r
3
3
70. Tfte Distributive Property-^
/<T~X
\f^\
ci(b ±c) = ab ± ac;
Example:3(7^2) =3x7^3 x2
(b + c)a = ba±ca
(7^2)3 = 7x3^2x3
Exercise 2: Use the given property to complete the statement.
a) The Commutative Property of Multiplication
5X2=2X?
b) The Associative Property of Multiplication
(2-5)-9 =2-(?-9)
c) TheJDistributive Property
2(3 +7) =6+7^- 7;
d) The Inverse Property of Addition
^
+ ? = 0
-in- 4=o
e) Identify the property that justifies the statement.
-3 + 3 = 0
Add Variable Expressions
Like terms are variable terms with the identical variable parts. Constants are like
terms.
"a,°"
i
i
Example: 9xy -4x> 3y - 1;- 2x,+ y- 2x^ +2, =• ^+(.\0) XWJ--^.-fC~0) Y+(3il} pm
like terms
•>
-
3a-
—
+4
- 7a-
+9
like terms
Exercise 3: Simplify:
a) 11*+ 9*= 20 )C
b) Sy-3y =
C) 7t2 +10t2 - 8t2 = ^^
z
d) 7w-3« + 10-h> =
\"-T v^J - 3 VA
e) Sy-3z-\2y + \\z =
(Jrl^V W-3+-H
-4 V + ?2.
2_
- a2 »^fX + I"b —X
1
Simplify Variable Expressions
Exercise 4: Simplify
a) (7a)(-3)= (.-V7) °~ - -Al^
^
b) (7x)2= d^erx) =^v (*•*; =^ x
L
c) (-36z)
—~^_/
H> F&'&
d) 7(llc-4)=
(i^-4)=
*- &7£
l7C-lg
e) -6(-x+7) =
rz.
f) C^-^^f-^j)^^
*+6)= 5as-£d-G>
g) 5a-(2
-(a+6)
- 'ba. -6
h) -3^+2(^+2>)-3(4a:+6>) =
-3x'4-_gyHK/ -J9X-I
-IS/ - iHy
i) -2x +2[5i +9(x +5)]-6=
'"^ V y l£x f ^y V^|0-U>