Algebra Class: Expressions & Phrases

Algebraic Expressions and Definitions

• A number increased by two: Represented as ( x + 2 )
• The product of nine and a number: Denoted as ( 9y )
• The quotient of nine and a number: Written as ( \frac{9}{y} )
• The difference of twice a number and five: Expressed as ( 2x - 5 )
• The sum of a number squared and ten: Denoted by ( x^2 + 10 )
• Six more than a number: Represented as ( x + 6 )
• Triple a number increased by twelve: Described as ( 3x + 12 )
• A number decreased by sixteen: Written as ( y - 16 )
• Double a number increased by five: Expressed as ( 2x + 5 )
• The sum of half a number and four: Represented as ( \frac{x}{2} + 4 )

Basic Operations and Terms

• The quotient of 11 and 9: Noted as ( \frac{11}{9} )
• The difference of 11 and 9: Calculated as ( 11 - 9 )
• The product of 11 and 9: Expressed as ( 11 \times 9 )
• The sum of 11 and 9: Denoted by ( 11 + 9 )

Powers and Variables

• A number squared: Represented as ( x^2 ) (e.g., ( 3 \times 3 ))
• A number cubed: Denoted as ( x^3 ) (e.g., ( 4 \times 4 \times 4 ))
• Coefficient: The number next to a variable
• Constant term: A number on its own without a variable
• Variable: A letter which stands in place of a number

Properties and Expressions

• Distributive Property: Illustrated as ( 3(a-4) = 3a - 12 )
• Fourteen less than a number: Represented as ( x - 14 )
• The difference of x and 3: Denoted by ( x - 3 )
• The quotient of 9 and the difference of x and p: Written as ( \frac{9}{(x - p)} )
• Ten less than the product of 4 and r: Expressed as ( 4r - 10 )
• Four times the sum of x and y: Represented as ( 4(x + y) )
• Four more than the product of 5 and y: Denoted by ( 5y + 4 )
• The product of 3 and the difference of x and 9: Written as ( 3(x - 9) )

These notes encapsulate key algebraic expressions and definitions to aid in understanding their meanings and applications.