What are Like Terms?

S6-SA1-0058

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Like terms are terms that have the exact same variables raised to the exact same powers. Only the numerical part (coefficient) can be different. Think of them as items of the same type that can be grouped together.

Simple Example

Quick Example

Imagine you have 3 cricket bats and your friend has 5 cricket bats. You can easily say you both have a total of 8 cricket bats because 'cricket bats' is the common item. Here, '3 bats' and '5 bats' are like terms because the 'bats' part is identical.

Worked Example

Step-by-Step

Let's identify like terms in the expression: 5x + 7y - 2x + 3x^2 + 4y

1. Look for terms with the variable 'x' raised to the power of 1: We have 5x and -2x.
---2. Look for terms with the variable 'y' raised to the power of 1: We have 7y and 4y.
---3. Look for terms with the variable 'x' raised to the power of 2: We have 3x^2.
---4. Group the identified like terms together.
---5. So, (5x, -2x) are like terms. (7y, 4y) are like terms. 3x^2 is a term by itself.
---Answer: The pairs of like terms are (5x, -2x) and (7y, 4y).

Why It Matters

Understanding like terms is crucial for simplifying complex equations, which is vital in fields like AI/ML for optimizing algorithms and in Physics for solving motion problems. Engineers use this to simplify formulas for building structures, and even doctors analyze data by grouping similar patient characteristics.

Common Mistakes

MISTAKE: Adding 3x and 2x^2 and getting 5x^3 | CORRECTION: 3x and 2x^2 are NOT like terms because the powers of 'x' are different (1 and 2). They cannot be directly added or subtracted.

MISTAKE: Thinking 4ab and 5a are like terms | CORRECTION: 4ab and 5a are NOT like terms because 4ab has two variables (a and b) while 5a only has one (a). All variables and their powers must match exactly.

MISTAKE: Forgetting the sign in front of a term when identifying like terms (e.g., seeing -7y as just 7y) | CORRECTION: Always consider the sign (+ or -) that comes before a term as part of that term. This is crucial for correct addition/subtraction.

Practice Questions

Try It Yourself

QUESTION: Are 6p and 9p like terms? | ANSWER: Yes

QUESTION: Identify the like terms in the expression: 2a + 5b - 3a + 7ab + 4b | ANSWER: (2a, -3a) and (5b, 4b)

QUESTION: From the list: 10x, 8x^2, -3x, 5y, 2x^2y, 7x^2, identify all terms that are like terms to 8x^2. | ANSWER: 7x^2

MCQ

Quick Quiz

Which of the following pairs are like terms?

4x and 4y

5a and 5a^2

7pq and -2qp

3m and 3

The Correct Answer Is:

Option C (7pq and -2qp) are like terms because 'pq' and 'qp' represent the same variables with the same powers (p^1q^1). The order of multiplication doesn't change the variables. Options A, B, and D have different variables or different powers.

Real World Connection

In the Real World

When a delivery app like Swiggy or Zomato calculates your total bill, it groups similar items. For example, '2 plates of idli' and '3 plates of idli' are like terms. The app adds them to show '5 plates of idli' before calculating the final amount, applying discounts, and adding delivery charges.

Key Vocabulary

Key Terms

VARIABLE: A symbol (usually a letter) representing an unknown value | COEFFICIENT: The numerical factor multiplying a variable (e.g., 5 in 5x) | TERM: A single number, variable, or product of numbers and variables (e.g., 3x, 7, -2y^2) | EXPONENT: A number indicating the power to which a base is raised (e.g., 2 in x^2)

What's Next

What to Learn Next

Now that you understand like terms, you're ready to learn 'Adding and Subtracting Algebraic Expressions'. This next step will show you how to combine these like terms to simplify much longer and more complex mathematical problems. You're building a strong foundation!