2.1.2 Simplifying and manipulating algebraic expressions

• What is an algebraic term composed of in an algebraic expression?

  Variable, coefficient, constant
• Match the term with its variable, coefficient, and constant:

  \( 3x \) ↔️ Variable: \( x \), Coefficient: 3, Constant: 0

  \( -5y \) ↔️ Variable: \( y \), Coefficient: -5, Constant: 0

  \( 2a + 7 \) ↔️ Variable: \( a \), Coefficient: 2, Constant: 7
• The constant in the term \( 2a + 7 \) is 2.


  False
• In the expression 4(x + 2), we multiply 4 by both x and 2.


  True
• Order the components of an algebraic term from left to right:

  1️⃣ Coefficient

  2️⃣ Variable

  3️⃣ Constant
• What is the coefficient in the term \( 3x \)?


  3
• How many like terms are in the expression \( 3x + 6 \)?

  Zero
• What is the result of multiplying 4 by (x + 2) using the distributive property?

  4x + 8
• The coefficient in the term \( 3x \) is 3.

  True
• A variable in an algebraic term is a letter that represents an unknown value.


  True
• Like terms must have the same variable and the same power.


  True
• What are like terms in algebraic expressions?

  Same variable, same power
• When using the distributive property, each term inside the parentheses is multiplied by the number outside


  True
• How do you combine like terms such as \( 3x + 5x \)?

  Add the coefficients
• The first step in using the distributive property is to multiply the term outside the parentheses by each term inside.


  True
• Steps to use the distributive property

  1️⃣ Multiply the number outside with each term inside

  2️⃣ Combine like terms (if necessary)
• What is the result of multiplying -2 by (3y - 5) using the distributive property?

  -6y + 10
• What is the simplified form of \( 3(x + 2) \)?

  \( 3x + 6 \)
• The expression \( -(a + 3) \) simplifies to \( -a - 3 \)

  True
• The exponent shows how many times the base is multiplied by itself


  True
• Match the exponent rule with its description:

  Product Rule ↔️ Add exponents when multiplying bases

  Quotient Rule ↔️ Subtract exponents when dividing bases

  Power Rule ↔️ Multiply exponents when raising a power to another exponent
• The combination of \( 4a \) and \( -6a \) results in \( -2a \).


  True
• The product rule can be written as \( a^m \times a^n = a^{m+n} \)


  True
• What is the result of combining \( 3x \) and \( -5x \)?

  \( -2x \)
• Combining like terms is always necessary when using the distributive property.

  False
• Steps to simplify \( (3x^2y)^3 \)

  1️⃣ Distribute the exponent to each term inside the parentheses

  2️⃣ Apply the power rule

  3️⃣ Simplify the expression
• What is the term for the entire expression when a base is raised to an exponent?

  Power
• What is the power rule for exponents?

  $(a^{m})^{n} =$$a^{m \times n}$
• Steps to combine terms with different signs

  1️⃣ Identify terms with the same variable

  2️⃣ Add their coefficients, keeping the sign of the larger number

  3️⃣ Write the result with the variable
• What is the simplified form of \( (3x^2y)^3 \)?

  $27x^{6}y^{3}$
• When simplifying \( (3x^2y)^3 \), the exponent 3 must be distributed to each term inside the parentheses


  True
• Steps to simplify expressions with parentheses

  1️⃣ Remove parentheses using the distributive property

  2️⃣ Combine like terms