What is a Term in an Algebraic Expression?

S6-SA1-0055

Grade Level:

Class 10

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

Definition

What is it?

In an algebraic expression, a 'term' is a single number, a single variable, or a product of numbers and variables. These terms are separated from each other by plus (+) or minus (-) signs.

Simple Example

Quick Example

Imagine you buy 3 notebooks and 2 pens. If a notebook costs 'x' rupees and a pen costs 'y' rupees, your total cost can be written as 3x + 2y. Here, '3x' is one term and '2y' is another term.

Worked Example

Step-by-Step

Let's find the terms in the expression: 5a - 7b + 10.

Step 1: Look at the expression: 5a - 7b + 10.
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Step 2: Identify the parts separated by '+' or '-' signs.
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Step 3: The first part is '5a'. This is a term.
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Step 4: The second part is '-7b'. Remember the sign goes with the term. So, this is a term.
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Step 5: The third part is '+10'. This is also a term.
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Answer: The terms in the expression 5a - 7b + 10 are 5a, -7b, and 10.

Why It Matters

Understanding terms helps you break down complex problems in engineering and science. For example, in AI, engineers use terms to build mathematical models for machine learning. Scientists use them to describe forces in physics or chemical reactions, helping them design everything from rockets to new medicines.

Common Mistakes

MISTAKE: Not including the sign with the term (e.g., in 2x - 3y, identifying terms as 2x, 3y) | CORRECTION: Always include the sign that comes before the term. So, the terms are 2x and -3y.

MISTAKE: Separating parts of a product (e.g., in 5xy, thinking 5, x, and y are separate terms) | CORRECTION: A product of numbers and variables (like 5xy) is considered one single term.

MISTAKE: Confusing terms with factors (e.g., in 3x, thinking 3 and x are terms) | CORRECTION: 3 and x are factors of the term 3x. The entire '3x' is the term itself.

Practice Questions

Try It Yourself

QUESTION: How many terms are there in the expression 4p + 9q - 1? | ANSWER: 3 terms (4p, 9q, -1)

QUESTION: List the terms in the expression 7x^2y - 12 + 5z. | ANSWER: 7x^2y, -12, 5z

QUESTION: Identify the terms in the expression (2/3)ab + c - 8mn + 5. | ANSWER: (2/3)ab, c, -8mn, 5

MCQ

Quick Quiz

Which of the following expressions has exactly two terms?

5x + 2y - 3

7ab

p - q

x^2 + y^2 + z^2

The Correct Answer Is:

Option C (p - q) has two parts separated by a minus sign, making them two terms. Options A and D have more than two terms, while Option B has only one term as 7ab is a single product.

Real World Connection

In the Real World

When you use a food delivery app like Swiggy or Zomato, the total bill calculation involves terms. For example, 'cost of food + delivery charge - discount coupon'. Each of these parts (food cost, delivery charge, discount) can be represented by terms in an algebraic expression used by the app's backend system.

Key Vocabulary

Key Terms

VARIABLE: A symbol, usually a letter, representing an unknown value. | CONSTANT: A fixed numerical value that does not change. | COEFFICIENT: The numerical factor of a term that contains a variable. | EXPRESSION: A combination of terms, numbers, and operations (like +, -, *, /).

What's Next

What to Learn Next

Great job understanding terms! Next, you should learn about 'Like and Unlike Terms'. Knowing this will help you simplify expressions, which is super important for solving algebraic equations and more complex math problems.