ALGEBRAIC EXPRESSION.CLEANED
Definition of Algebraic Expression
An algebraic expression is a mathematical phrase made from numbers, variables (like x or n), and operations such as addition, subtraction, multiplication, division, and exponents. It does not include an equals sign.
Why algebraic expressions matter
- They let you describe patterns and real-world situations with variables.
- They are the building blocks for equations, formulas, and functions.
- You use them in geometry, physics, finance, coding, and more.
Parts of an algebraic expression
Here’s what to look for inside an expression:
- Variable: a letter that stands for an unknown value (example: x, n).
- Coefficient: a number multiplying a variable (in 7x, the coefficient is 7).
- Term: a single piece separated by + or − signs (3x is a term, -5 is a term).
- Constant: a number with no variable (example: 12).
- Operator: symbols like +, −, ×, ÷, ^.
Examples of algebraic expressions
Simple: x + 5, 3n, 12 - y
Multi-term: 2x + 7, 5a - 3b + 9
With exponents: x<sup>2</sup> + 4x + 4
With parentheses: 3(x - 2)
Like terms (a key idea)
Like terms have the same variable part (same letters with the same exponents). You can combine only like terms.
- 3x and 5x are like terms → 3x + 5x = 8x
- 2x and 2x<sup>2</sup> are not like terms.
- 7ab and -3ab are like terms → 4ab
Evaluating an expression
To evaluate an expression, substitute a value for the variable and compute.
Example: Evaluate 2x + 3 when x = 4.
2(4) + 3 = 8 + 3 = 11
Simplifying an expression
To simplify, combine like terms and use order of operations.
Example: Simplify 4x + 3 - 2x + 9.
Combine like terms: (4x - 2x) + (3 + 9) = 2x + 12
Common mistakes
- Combining unlike terms: x + x<sup>2</sup> cannot become 2x<sup>2</sup> (that’s wrong).
- Forgetting parentheses: 3(x - 2) means multiply both terms → 3x - 6.
- Confusing an expression with an equation: expressions have no equals sign.
Quick practice (with answers)
- Simplify: 6y + 2 - 3y + 5
- Evaluate: n<sup>2</sup> - 4 when n = 5
- Are these like terms? 2ab and -7ba
Answers: 1) 3y + 7 2) 21 3) Yes (same letters)
Video example: Algebraic expressions
Solved examples
Question: A shop charges $5 for renting a video cassette for the first day. It charges $2 extra for every additional day. Which expression gives the total cost for n days?
Choices:
A. 3 + 2n
B. 5n + 2
C. n
D. 5 - 2n
Correct Answer: A
Solution
Day 1 costs $5. The remaining n-1 days cost 2 dollars each.
Total: 5 + 2(n - 1) = 5 + 2n - 2 = 3 + 2n
Quick Summary
- Algebraic expressions use variables to represent unknown values.
- They are building blocks for equations and formulas.
- Key components include variables, coefficients, terms, constants, and operators.
- Like terms can be combined to simplify expressions.
🍎 Teacher Insights
Emphasize the importance of understanding the definitions of key terms (variable, coefficient, term, constant). Use real-world examples to illustrate the use of algebraic expressions. Provide ample practice opportunities for simplifying and evaluating expressions.🎓 Prerequisites
- Basic arithmetic operations (addition, subtraction, multiplication, division)
- Understanding of variables
- Order of operations (PEMDAS/BODMAS)
Check Your Knowledge
Q1: Simplify the expression: 6y + 2 - 3y + 5
Q2: Evaluate the expression: n² - 4 when n = 5
Q3: Which of the following are like terms?
Frequently Asked Questions
Q: What is the difference between an expression and an equation?
A: An expression is a mathematical phrase without an equals sign, while an equation shows the equality between two expressions using an equals sign.
Q: How do I simplify an algebraic expression?
A: Combine like terms (terms with the same variable part) using addition and subtraction, and follow the order of operations.