3.2 Advanced Algebra

• What does it mean to simplify an algebraic expression?

  Combine like terms
• The distributive property is used to remove brackets in algebraic expressions.


  True
• To check the solution of a linear equation, substitute the value of the variable back into the original equation.

  True
• To simplify an algebraic expression, we combine like terms
• Match each step in simplifying an algebraic expression with its description:

  Combine like terms ↔️ Identify and add coefficients of identical variables

  Remove brackets ↔️ Use the distributive property to expand expressions

  Apply distributive property ↔️ Multiply coefficients outside brackets with terms inside
• The distributive property involves multiplying a coefficient outside the brackets with the terms inside.
• To solve a linear equation, you must isolate the variable using inverse operations.


  True
• Steps to solve a linear equation

  1️⃣ Simplify the equation

  2️⃣ Isolate the variable

  3️⃣ Check the solution
• After isolating a variable in the substitution method, we substitute its expression into the other equation.
• To evaluate an algebraic expression, we substitute specific values for the variables
• What is the first step in solving a linear equation?

  Simplify the equation
• Match each operation with its inverse operation:

  Addition ↔️ Subtraction

  Subtraction ↔️ Addition

  Multiplication ↔️ Division

  Division ↔️ Multiplication
• To evaluate an algebraic expression, we perform calculations after substituting values for the variables.


  True
• To simplify an algebraic expression, we combine like terms.
• Simplifying expressions involves combining like terms and removing brackets.


  True
• What is the simplified form of the expression 2(x + 3) - 4x?

  -2x + 6
• Match the operation with its inverse operation:

  Addition ↔️ Subtraction

  Subtraction ↔️ Addition

  Multiplication ↔️ Division

  Division ↔️ Multiplication
• Simultaneous equations can be solved using the substitution or elimination method.


  True
• What are the solutions to the simultaneous equations x + y = 5 and 2x - y = 1?

  x = 2, y = 3
• In the substitution method, the first step is to isolate one variable
• In the elimination method, equations are added or subtracted to eliminate one variable
• What is an algebraic expression?

  Variables, coefficients, and operations
• Match the process with its description:

  Simplifying ↔️ Combining like terms

  Evaluating ↔️ Substituting values for variables
• Combining like terms in `2x + 6 - 4x` results in `-2x + 6`.


  True
• Steps to simplify an algebraic expression

  1️⃣ Combine like terms

  2️⃣ Remove brackets

  3️⃣ Apply the distributive property
• The inverse operation of addition is subtraction
• Steps to solve a linear equation

  1️⃣ Simplify the equation

  2️⃣ Isolate the variable

  3️⃣ Check the solution
• What property is used to expand brackets in algebraic expressions?

  Distributive property
• To evaluate an algebraic expression, we substitute specific values for the variables.
• When combining like terms, we add their coefficients together.
• Steps to simplify an algebraic expression

  1️⃣ Combine like terms

  2️⃣ Remove brackets

  3️⃣ Apply the distributive property
• What is the solution to the equation 3x + 5 = 14?

  x = 3
• The substitution method involves isolating one variable in one equation.
• Steps to solve simultaneous equations using elimination

  1️⃣ Multiply equations to match coefficients

  2️⃣ Add or subtract equations

  3️⃣ Solve for the remaining variable

  4️⃣ Substitute back to find the other variable

  5️⃣ Check the solution
• The substitution method requires solving for both variables simultaneously.

  False
• The final step in the elimination method is to substitute back to find the other variable.


  True
• The first step in factorizing is to identify the largest common factor
• When factorizing 4a^2 + 12ab, the largest common factor is 4a
• What does factorizing algebraic expressions involve?

  Expressing as a product
• What is the largest common factor of 3x^2 - 9x?

  3x