2.1 Notation, Vocabulary, and Manipulation

• What is a variable in an algebraic expression?

  Symbol representing unknown values
• What is the numerical factor multiplying a variable called?

  Coefficient
• What are the constants in the expression `5x + 3y - 2`?

  -2
• When multiplying powers with the same base, you add the exponents
• What are like terms in algebraic expressions?

  Terms with same variable(s) and exponent(s)
• Exponents indicate how many times to multiply a base number by itself
• What is the result of adding like terms in the expression `2x + 3x`?

  5x
• Like terms in algebraic expressions must have the same variable(s) and exponent(s).


  True
• What is the first step in multiplying algebraic expressions?

  Apply distributive property
• Divide the algebraic expression: `(8x² + 4x) / (2x)`

  4x + 2
• Expand the brackets in the expression: `3(2x + 4)`

  6x + 12
• The greatest common factor (GCF) is the largest factor that divides all terms evenly.


  True
• An algebraic expression combines numbers, variables, and arithmetic operations
• Constants in algebraic expressions are fixed numerical values
• In the algebraic expression `3x + 5`, the term `3x` combines a number and a variable
• What is the value of 3²?

  9
• Adding like terms involves combining their coefficients.

  True
• Combining like terms in subtraction involves subtracting their coefficients
• Match the algebraic component with its definition:

  Variables ↔️ Symbols representing unknown values

  Constants ↔️ Fixed numerical values

  Coefficients ↔️ Numerical factors multiplying variables
• When dividing powers with the same base, you subtract the exponents
• Simplify the algebraic expression: `2x + 3y + 4 + 5x - y + 2`

  7x + 2y + 6
• Simplify the algebraic expression: `2x + 3y + 4 + 5x - y + 2`

  7x + 2y + 6
• Multiply the algebraic expression: `2x * (3x + 4)`

  6x² + 8x
• Evaluate the expression using PEMDAS: `12 ÷ (4 + 2) * 3 - 1`

  5
• To expand brackets, you multiply each term inside by the factor outside.


  True
• Factorize the algebraic expression: `4x + 12`

  
  

  
  

  4(x + 3)
• In the algebraic expression `3x + 5`, the number `3` is a coefficient.

  True
• In the expression `5x + 3y - 2`, the constant is `-2`.


  True
• Match the exponent notation with its definition:

  Base ↔️ The number being multiplied

  Exponent ↔️ Indicates how many times to multiply the base
• What are like terms in algebraic expressions?

  Terms with same variable and exponent
• Combining like terms in addition involves adding their coefficients.

  True
• What arithmetic operations are used in algebraic expressions?

  Addition, subtraction, multiplication, division
• When multiplying powers with the same base, you add the exponents.


  True
• When subtracting like terms, you subtract their coefficients
• Adding like terms involves combining their coefficients
• When dividing algebraic expressions with the same base, you subtract their exponents
• Steps in the order of operations (PEMDAS)

  1️⃣ Parentheses/Brackets

  2️⃣ Exponents/Orders

  3️⃣ Multiplication and Division

  4️⃣ Addition and Subtraction
• The order of operations is often remembered by the acronym PEMDAS
• What is the first operation performed in the expression `(3 + 2) * 4` according to PEMDAS?

  Addition within parentheses
• Expanding brackets involves applying the distributive law.