Say it With Symbols – Notes – Investigation 1
Expression – a mathematical phrase that combines numbers and or variables using mathematical operations.
Numerical Expressions Variable ( Algebraic ) Expressions
6x
4 + 2x + 5
3 ( 2 ) – 47x - 3
5 + 3 ( 8 )2x + y
Equation – a mathematical statement that sets an expression equal to another expression
Numerical EquationsVariable ( Algebraic ) Equations
5 + 4 = 9x + 5 = 9
3 ( 2 ) – 5 = 13X + 7 = 2X – 6
Variable expressions are evaluated.
Example: 2x + 5, let x = 6,
Substitute 6 for x 2 ( 6 ) + 5
12 + 5
17
Variable equations are solved.
Example: 3x + 2 = 11
- 2 - 2
3x = 9
3 3
X = 3
Commutative property of addition: a + b = b + a 3 + 2 = 2 + 3
Commutative property of multiplication: a(b) = (b)a 6 (7) = ( 7) 6
Distributive Property ( addition and subtraction )
a ( b + c ) = ab + ac for addition a ( b – c ) = ab – ac for subtraction
3 ( 2 + 5 ) = 3 (2) + 3 ( 5 ) which simplifies to 6 + 15 = 21
4 ( 6 – 2 ) = 4(6) – 4(2) which simplifies to 24 – 8 = 16
3 ( x + 5 ) = 3x + 3(5) or 3x + 15 5 ( x – 2 ) = 5x – 5(2) or 5x – 10
Factored Form Expanded Form Simplified Form
( x + 2 ) ( x + 5 ) = x2 + 2x + 5x + 10 = x2 + 7x + 10 NOTE: 2 + 5 = 7, ( 2) ( 5 ) = 10
( x + 4 ) ( x + 6 ) = x2 + 4x + 6x + 24 = x2 + 10x + 24 NOTE: 4 + 6 = 10, ( 4) ( 6 ) = 24
(x + 6 ) ( x + 7 ) = x2 + 6x + 7x + 42 = x2 + 13x + 42 NOTE: 6 + 7 = 13, ( 6) ( 7 ) = 42
( x + 1 ) ( x + 9 ) = x2 + 1x + 9x + 9 = x2 + 10x + 9 NOTE: 1 + 9 = 10, ( 1) ( 9 ) = 9
Expanded Form Factored Form
X2 + 5x + 4 = ( x + 1 ) ( x + 4 ) because 4 + 1 = 5 and ( 4 ) ( 1 ) = 4
X2 + 9x + 20 = ( x + 5 ) ( x + 4 ) because 4 + 5 = 9 and ( 4 ) ( 5 ) = 20
X2 + 10x + 16 = ( x + 2 ) ( x + 8 ) because 2 + 8 = 10 and ( 2 ) ( 8 ) = 16
X2 + 7x + 10 = ( x + 2 ) ( x + 5 ) because 2 + 5 = 7 and ( 2 ) ( 5 ) = 10