ALGEBRAIC EXPRESSION
EXPRESSIONS IN ACTION: A JOURNEY THROUGH ALGEBRA
🔍 Introduction: Why Do We Need Algebraic Expressions?
Imagine you run a business, and your monthly earnings change based on the number of customers you get. If each customer pays ₹50, then:
✔ If you get 10 customers, you earn ₹500
✔ If you get 100 customers, you earn ₹5000
Instead of writing each case separately, we can use an Algebraic Expression:
Earnings=50×x
where x is the number of customers.
📌 Real-Life Uses of Algebraic Expressions:
✅ Finding total cost while shopping
✅ Calculating profits in a business
✅ Predicting scores in exams based on correct answers
🧩 What is an Algebraic Expression?
An Algebraic Expression is a mathematical phrase that includes:
✔ Numbers (like 2, 3, 5)
✔ Variables (like x, y, z)
✔ Operations (+, -, ×, ÷)
📌 Example: 3x+5y−7
Here,
✔ 3x means 3 multiplied by x
✔ 5y means 5 multiplied by y
✔ -7 is a constant
📂 Parts of an Algebraic Expression
Every algebraic expression has three main parts:
|
Term |
Example |
Definition |
|
Variables |
x, y, z |
Letters that represent unknown values |
|
Constants |
5, -7, 10 |
Fixed numbers that don’t change |
|
Coefficients |
3 in 3x, -5 in -5y |
Numbers multiplied with variables |
📌 Example Breakdown:
Expression: 4x² + 3y – 5
✔ 4x² → Coefficient: 4, Variable: x²
✔ 3y → Coefficient: 3, Variable: y
✔ -5 → Constant
📊 Types of Algebraic Expressions
1️⃣ Monomial:
✔ Only 1 term
✔ Example: 5x, -3y², 7
2️⃣ Binomial:
✔ Two terms separated by + or –
✔ Example: 3x + 2y, 5a – 4b
3️⃣ Trinomial:
✔ Three terms separated by + or –
✔ Example: x² + 4x – 6, 2a + 3b – 5
4️⃣ Polynomial:
✔ More than three terms
✔ Example: 4x³ + 2x² – 3x + 7
📌 Memory Trick:
🟢 Mono = 1 (One term)
🟢 Bi = 2 (Bicycle has 2 wheels)
🟢 Tri = 3 (Tricycle has 3 wheels)
🟢 Poly = Many
🎯 Operations on Algebraic Expressions
➕ Addition of Expressions
✔ Step 1: Arrange like terms together
✔ Step 2: Add coefficients
🔹 Example:
(3x+2y)+(5x−4y)
✔ Combine like terms → (3x + 5x) + (2y – 4y)
✔ Answer: 8x – 2y
➖ Subtraction of Expressions
✔ Step 1: Arrange like terms together
✔ Step 2: Subtract coefficients
🔹 Example:
(7x+3y)−(4x+2y)
✔ Combine like terms → (7x – 4x) + (3y – 2y)
✔ Answer: 3x + y
✖ Multiplication of Expressions
✔ Multiply coefficients and add exponents
🔹 Example:
(3x)×(2y)
✔ Multiply numbers → 3 × 2 = 6
✔ Multiply variables → xy
✔ Answer: 6xy
➗ Division of Expressions
✔ Divide coefficients and subtract exponents
🔹 Example:
6x^2/3x
✔ Divide numbers → 6 ÷ 3 = 2
✔ Subtract powers of x → x² ÷ x = x
✔ Answer: 2x
🏆 Special Algebraic Identities (Smart Tricks!)
📌 Formula 1: (a + b)² = a² + 2ab + b²
🔹 Example: (x + 3)² = x² + 6x + 9
📌 Formula 2: (a – b)² = a² – 2ab + b²
🔹 Example: (y – 5)² = y² – 10y + 25
📌 Formula 3: (a + b)(a – b) = a² – b²
🔹 Example: (x + 4)(x – 4) = x² – 16
📌 Trick to Remember:
✔ “Square of sum = First² + 2AB + Second²”
✔ “Square of difference = First² – 2AB + Second²”
✔ “Sum-Difference Shortcut = First² – Second²”
🌍 Real-Life Uses of Algebraic Expressions
✔ Physics: Calculating speed, distance, and time
✔ Banking: Interest formulas involve algebra
✔ Computer Science: Programming uses variables and expressions
✔ Business: Profit calculations use expressions
ALGEBRAIC EXPRESSIONS – 50 MCQs
🔹 Questions (1–50)
📘 Basic Concepts (1–10)
- An algebraic expression contains:
A) Only numbers
B) Only variables
C) Numbers, variables, operations
D) Only symbols - In 3x + 5, x is:
A) Constant
B) Variable
C) Coefficient
D) Number - In 7y, 7 is:
A) Variable
B) Constant
C) Coefficient
D) Term - A fixed value is called:
A) Variable
B) Constant
C) Expression
D) Equation - Which is an algebraic expression?
A) 5 + 3
B) 2x + 7
C) 9
D) 4 × 2 - In 4x², the variable is:
A) 4
B) x
C) 2
D) x² - Number of terms in 3x + 5y – 2 =
A) 2
B) 3
C) 4
D) 1 - A term without variable is:
A) Variable
B) Constant
C) Coefficient
D) Expression - In -5y, coefficient is:
A) -5
B) y
C) 5
D) -y - Expression: 6x + 2y – 3 has:
A) 1 term
B) 2 terms
C) 3 terms
D) 4 terms
📘 Types of Expressions (11–20)
- Expression with one term is:
A) Binomial
B) Monomial
C) Trinomial
D) Polynomial - Example of monomial:
A) 3x
B) x + y
C) x² + y
D) a + b + c - Expression with two terms:
A) Monomial
B) Binomial
C) Trinomial
D) Polynomial - Example of binomial:
A) 5x
B) 3x + 2
C) x² + y + z
D) 7 - Expression with three terms:
A) Monomial
B) Binomial
C) Trinomial
D) Polynomial - Example of trinomial:
A) x² + 2x + 1
B) 3x
C) 5 + x
D) 7 - Polynomial means:
A) One term
B) Two terms
C) Many terms
D) No terms - Example of polynomial:
A) 2x
B) x + y
C) x² + 2x + 3 + y
D) 5 - Number of terms in 4x³ + 2x² – x + 7 =
A) 2
B) 3
C) 4
D) 5 - Which is not a polynomial?
A) 3x²
B) x + 2
C) 5
D) 1/x
📘 Operations (21–35)
- (3x + 2y) + (5x – 4y) =
A) 8x – 2y
B) 2x + 6y
C) 8x + 6y
D) 2x – 2y - (7x + 3y) – (4x + 2y) =
A) 3x + y
B) 11x + 5y
C) 3x – y
D) x + y - Like terms are:
A) Same variables & powers
B) Different variables
C) Only numbers
D) Only variables - 2x + 3x =
A) 5
B) 5x
C) 6x
D) x - 5y – 2y =
A) 3
B) 3y
C) 7y
D) y - (3x)(2y) =
A) 6xy
B) 5xy
C) xy
D) 6x - (6x²) ÷ (3x) =
A) 2x
B) 3x
C) 2x²
D) x - Multiply: 2x × 3x =
A) 6x
B) 6x²
C) 5x²
D) x² - Add: x + x + x =
A) x
B) 2x
C) 3x
D) x² - Subtract: 9x – 4x =
A) 5
B) 5x
C) 13x
D) x - (a + b) + (a – b) =
A) 2a
B) 2b
C) a
D) b - (2x + 3) – (x + 1) =
A) x + 2
B) x + 4
C) 2x + 2
D) x – 2 - (x)(x) =
A) x
B) 2x
C) x²
D) x³ - Divide: 8x² ÷ 2x =
A) 4x
B) 4x²
C) 2x
D) x - (3x)(4x²) =
A) 12x²
B) 12x³
C) 7x³
D) x³
📘 Identities & Applications (36–50)
- (a + b)² =
A) a² + b²
B) a² + 2ab + b²
C) a² – b²
D) 2ab - (a – b)² =
A) a² – 2ab + b²
B) a² + b²
C) a² – b²
D) 2ab - (a + b)(a – b) =
A) a² + b²
B) a² – b²
C) 2ab
D) ab - (x + 3)² =
A) x² + 6x + 9
B) x² + 9
C) x² + 3x
D) x² – 9 - (y – 5)² =
A) y² – 10y + 25
B) y² + 25
C) y² – 25
D) y² + 10y - (x + 4)(x – 4) =
A) x² – 16
B) x² + 16
C) x² + 8x
D) x² – 8x - x² – 9 =
A) (x + 3)²
B) (x – 3)²
C) (x + 3)(x – 3)
D) x(x – 9) - Value of 2x when x = 3 =
A) 5
B) 6
C) 9
D) 3 - Value of x + y when x=2, y=3 =
A) 5
B) 6
C) 4
D) 3 - Algebra is used in:
A) Business
B) Science
C) Banking
D) All - Expression for ₹50 per item =
A) 50
B) x + 50
C) 50x
D) x/50 - Variable represents:
A) Fixed value
B) Unknown value
C) Constant
D) Number - Coefficient of x in 5x =
A) 5
B) x
C) 1
D) 0 - Expression means:
A) Sentence
B) Equation
C) Mathematical phrase
D) Value - Simplify: (5x + 2y) + (3x – 4y) =
A) 8x – 2y
B) 2x + 6y
C) 8x + 6y
D) 2x – 2y
✅ ANSWER KEY
1-C, 2-B, 3-C, 4-B, 5-B,
6-B, 7-B, 8-B, 9-A, 10-C,
11-B, 12-A, 13-B, 14-B, 15-C,
16-A, 17-C, 18-C, 19-C, 20-D,
21-A, 22-A, 23-A, 24-B, 25-B,
26-A, 27-A, 28-B, 29-C, 30-B,
31-A, 32-A, 33-C, 34-A, 35-B,
36-B, 37-A, 38-B, 39-A, 40-A,
41-A, 42-C, 43-B, 44-A, 45-D,
46-C, 47-B, 48-A, 49-C, 50-A
