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Questions and Answers
What is an algebraic expression?
What is an algebraic expression?
An expression that contains numbers, operations, and one or more symbols.
Which of the following is an example of an algebraic expression?
Which of the following is an example of an algebraic expression?
- 145
- 2n + 5 (correct)
- 8x + 15 = 55
- 3/4
Which of the following is NOT an example of an algebraic expression?
Which of the following is NOT an example of an algebraic expression?
- 5n³ ÷ 6y²
- 3 - 8d²
- 2n + 5
- 8x + 15 = 55 (correct)
What are the parts of an algebraic expression called?
What are the parts of an algebraic expression called?
What are letters that represent one or more unknown numbers called?
What are letters that represent one or more unknown numbers called?
What is the numerical factor of a term that contains a variable called?
What is the numerical factor of a term that contains a variable called?
What are the terms called that do not contain a variable?
What are the terms called that do not contain a variable?
What does the expression n⁵ mean?
What does the expression n⁵ mean?
Identify the base and exponent in the expression: 5x⁴
Identify the base and exponent in the expression: 5x⁴
Identify the terms, coefficients, and constants in the expression: 12 + 10c.
Identify the terms, coefficients, and constants in the expression: 12 + 10c.
Identify the terms, coefficients, and constants in the expression: 15 + 3w + ½.
Identify the terms, coefficients, and constants in the expression: 15 + 3w + ½.
Identify the terms, coefficients, and constants in the expression: z² + 9w - 2.
Identify the terms, coefficients, and constants in the expression: z² + 9w - 2.
Identify the terms, coefficients, and constants in the expression: 6r(8r - 13).
Identify the terms, coefficients, and constants in the expression: 6r(8r - 13).
Identify the terms, coefficients, and constants in the expression: 4x² - 7y + ¾.
Identify the terms, coefficients, and constants in the expression: 4x² - 7y + ¾.
Identify the terms, coefficients, and constants in the expression: 2x(x - 3y + 4).
Identify the terms, coefficients, and constants in the expression: 2x(x - 3y + 4).
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Study Notes
Algebraic Expression Fundamentals
- An algebraic expression consists of numbers, operations, and one or more symbols.
- Examples of algebraic expressions include:
- 2n + 5
- 6(4d)
- 2 - 8d²
- 5n³ ÷ 6y²
Non-Examples
- Non-examples exclude expressions that are not algebraic, such as:
- Standalone numbers (e.g., 145)
- Equations (e.g., 8x + 15 = 55)
- Fractions (e.g., ¾)
- Equalities with algebraic terms (e.g., 3x³ ÷ 4y² = 124)
Components of Algebraic Expressions
- Parts of an algebraic expression are called terms.
- Terms are separated by addition or subtraction signs, illustrated by the expression 3 + 2x + 7y, which consists of three terms: 3, 2x, and 7y.
Variables and Coefficients
- Variable: Letters representing one or more unknown numbers (e.g., in 3 + 2x + 7y, x and y are variables).
- Coefficient: The numerical factor of a term with a variable (in 3 + 2x + 7y, coefficients are 2 and 7).
Constants
- A constant is a term without a variable. Example: In 3 + 2x + 7y, the constant is 3.
Exponents
- The expression n⁵ represents n multiplied by itself five times: n × n × n × n × n.
- In the expression 5x⁴, the base is x and the exponent is 4 (with 5 as the coefficient).
Analyzing Expressions
- Terms, coefficients, and constants breakdown:
- For 12 + 10c:
- Terms: 12, 10c
- Coefficient: 10
- Constant: 12
- For 15 + 3w + ½:
- Terms: 15, 3w, ½
- Coefficient: 3
- Constants: 15, ½
- For z² + 9w - 2:
- Terms: z², 9w, -2
- Coefficients: 9, 1 (in front of z)
- Constant: -2
- For 6r(8r - 13):
- Terms: 8r, 13
- Coefficients: 6, 8
- Constant: 13
- For 4x² - 7y + ¾:
- Terms: 4x², -7y, ¾
- Coefficients: 4, -7
- Constant: ¾
- For 2x(x - 3y + 4):
- Terms: x, -3y, 4
- Coefficient: 2, 1 (in front of x)
- Constant: 4
- For 12 + 10c:
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