2.1 Notation, Vocabulary, and Manipulation

• Algebraic notation refers to the symbolic representation of mathematical quantities and relationships
• A symbol (usually a letter) representing an unknown or changing quantity is called a variable
• An expression is a combination of terms connected by operators
• What is the process of identifying and extracting common factors called?

  Factoring
• Match the algebraic concept with its description:

  Combining like terms ↔️ Adding coefficients of terms with the same variable

  Simplifying expressions ↔️ Making expressions more concise

  Coefficients ↔️ Numerical factors multiplying variables

  Expressions ↔️ Combinations of terms joined by operators
• Simplifying expressions makes them more concise and easier to work with.


  True
• Expressions are combinations of terms joined by operators like +, -, *, /


  True
• Steps to simplify the algebraic expression 3x + 2y - x + 5y

  1️⃣ Combine like terms with x: 3x - x = 2x

  2️⃣ Combine like terms with y: 2y + 5y = 7y

  3️⃣ Write the simplified expression: 2x + 7y
• Rewriting expressions in a more concise or useful way is crucial for solving algebraic problems.


  True
• What does algebraic notation refer to?

  Symbolic representation of math
• Constants in algebraic notation are fixed numerical values.


  True
• A constant in algebra is a fixed numerical value
• An expression in algebra is a combination of terms connected by operators
• Factoring in algebra involves identifying and extracting common factors
• What is a common mistake during expansion in algebra?

  Forgetting to multiply all terms
• What is the result of expanding 3(x + 2)?

  3x + 6
• Match the algebraic operation with its example:

  Expanding brackets ↔️ 3(x + 2) = 3x + 6

  Simplifying powers ↔️ x² * x³ = x⁵
• To expand 2(x + 3), the result is 2x + 6
• When combining like terms, we add their coefficients.


  True
• Factoring involves identifying and extracting common factors from the terms.
• When factoring, we rewrite an expression as a product of its common factors.


  True
• Steps to solve the inequality 2x + 3 < 7

  1️⃣ Subtract 3 from both sides: 2x < 4

  2️⃣ Divide both sides by 2: x < 2
• What do coefficients represent in algebraic notation?

  Numerical factors multiplying variables
• What does algebraic notation refer to?

  Symbolic representation of relationships
• What is an example of a constant in algebraic notation?

  2
• Expressions are combinations of terms joined by operators
• What is the result of combining like terms in the expression `2x + 3x`?

  5x
• Simplifying expressions makes them easier to work with.

  True
• Factorization involves rewriting an expression as a product
• What is the simplified form of `x² * x³`?

  x⁵
• What symbols are used to compare expressions in inequalities?

  <, >, ≤, ≥
• What is the solution to the inequality `2x < 4`?

  x < 2
• A term in algebraic notation is a single variable, constant, or their combination
• What is the definition of a variable in algebra?

  Symbol representing unknown quantity
• A term in algebra can be a single number, variable, or their product.


  True
• Expanding in algebra involves multiplying a coefficient to all terms inside parentheses.


  True
• Match the algebraic technique with its description:

  Expansion ↔️ Distributes a coefficient over terms inside parentheses

  Factorization ↔️ Identifies and extracts common factors from terms
• Systematically checking all factors when factorizing ensures accuracy
• Adding exponents instead of multiplying them is a common mistake when simplifying powers
• To expand an expression with brackets, distribute the coefficient outside the brackets to each term inside.


  True