Inaugurated by IN-SPACe
ISRO Registered Space Tutor
S3-SA1-0333
What is Simplifying Expressions by Combining Like Terms?
Grade Level:
Class 7
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
Simplifying expressions by combining like terms means making an algebraic expression shorter and easier to understand by grouping together terms that are similar. 'Like terms' are terms that have the exact same variables raised to the exact same powers. For example, 3x and 5x are like terms, but 3x and 5x^2 are not.
Simple Example
Quick Example
Imagine you're buying fruits at the market. You buy 3 apples and 2 bananas. Later, you buy 4 more apples and 1 more banana. Instead of saying you have '3 apples + 2 bananas + 4 apples + 1 banana', you can combine the 'like fruits' to say you have '7 apples + 3 bananas'. This makes it much simpler to know your total.
Worked Example
Step-by-Step
Let's simplify the expression: 5a + 3b - 2a + 7b - 4
1. Identify like terms. Terms with 'a' are 5a and -2a. Terms with 'b' are 3b and 7b. The number -4 is a constant term.
---2. Group the like terms together: (5a - 2a) + (3b + 7b) - 4
---3. Combine the 'a' terms: 5a - 2a = 3a
---4. Combine the 'b' terms: 3b + 7b = 10b
---5. The constant term -4 remains as it is, as there are no other constant terms to combine it with.
---6. Put the combined terms back together: 3a + 10b - 4
ANSWER: The simplified expression is 3a + 10b - 4
Why It Matters
Simplifying expressions is like tidying up your room – it makes everything clearer and easier to use! In fields like Computer Science and Data Science, this skill helps write efficient code and algorithms. Engineers use it to simplify complex equations for designing bridges or rockets, saving time and preventing errors.
Common Mistakes
MISTAKE: Combining unlike terms, like adding 3x and 2y to get 5xy. | CORRECTION: Only terms with the exact same variables and powers can be combined. 3x and 2y are different, so they cannot be added.
MISTAKE: Forgetting the sign in front of a term when moving it or combining it, e.g., in 4x - 2y + 3x, combining 4x and 3x but treating -2y as +2y. | CORRECTION: Always include the sign (plus or minus) that is directly in front of the term when grouping or combining it.
MISTAKE: Incorrectly combining terms with different powers, e.g., adding 2x and 3x^2 to get 5x^3 or 5x. | CORRECTION: Terms like 2x and 3x^2 are NOT like terms because the powers of 'x' are different (x^1 vs. x^2). They cannot be combined.
Practice Questions
Try It Yourself
QUESTION: Simplify: 7m + 2n - 3m + 5n | ANSWER: 4m + 7n
QUESTION: Simplify: 10p - 4q + 2p - 6q + 3 | ANSWER: 12p - 10q + 3
QUESTION: Simplify: 5x^2 + 3x - 2x^2 + 7x - 1 | ANSWER: 3x^2 + 10x - 1
MCQ
Quick Quiz
Which of the following expressions is the simplified form of 6a + 8b - 2a - 3b?
4a + 5b
8a + 11b
4a - 5b
8a - 11b
The Correct Answer Is:
A
To simplify, combine 6a - 2a to get 4a, and combine 8b - 3b to get 5b. So, the simplified expression is 4a + 5b.
Real World Connection
In the Real World
Imagine a cricket coach calculating total runs. If a player scored 'x' runs in 3 matches and 'y' runs in 2 matches, and another player scored '2x' runs in 4 matches and '3y' runs in 1 match, combining like terms helps the coach quickly find the total 'x' runs and 'y' runs scored across both players, making analytics easier for strategy building.
Key Vocabulary
Key Terms
TERM: Like Terms: Terms that have the exact same variables raised to the exact same powers, like 5x and -2x. | TERM: Expression: A combination of numbers, variables, and operation signs. | TERM: Variable: A symbol (usually a letter) representing an unknown value. | TERM: Constant: A term in an expression that has a fixed value and no variable.
What's Next
What to Learn Next
Great job learning to simplify expressions! Next, you can explore 'Solving Linear Equations'. This skill builds on combining like terms, as you'll often need to simplify equations before you can find the value of the unknown variable. Keep practicing!
