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What is Expanding a Simple Bracket (3(x+2))?
Grade Level:
Class 5
Maths, Computing, AI, Physics
Definition
What is it?
Expanding a simple bracket means multiplying the number or term outside the bracket by each term inside the bracket. It helps us remove the brackets and write the expression in a simpler form. The main idea is to distribute the multiplication.
Simple Example
Quick Example
Imagine you have 3 packets of laddoos, and each packet has (5 motichoor laddoos + 2 boondi laddoos). To find the total number of each type of laddoo, you multiply 3 by 5 AND 3 by 2. So, you have (3 x 5) motichoor laddoos + (3 x 2) boondi laddoos.
Worked Example
Step-by-Step
Let's expand 4(y + 7).
1. Identify the number outside the bracket: It's 4.
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2. Identify the terms inside the bracket: They are 'y' and '+ 7'.
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3. Multiply the number outside by the first term inside: 4 * y = 4y.
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4. Multiply the number outside by the second term inside: 4 * 7 = 28.
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5. Combine the results, keeping the sign: 4y + 28.
Answer: 4y + 28
Why It Matters
Expanding brackets is a basic step in solving many complex problems in Maths, Physics, and even Computer Science. Engineers use it to design structures, game developers use it for character movements, and data scientists use it to simplify equations. It's a foundational skill for future studies and careers.
Common Mistakes
MISTAKE: Multiplying only the first term inside the bracket. For example, 3(x + 2) becomes 3x + 2. | CORRECTION: Remember to multiply the number outside by EVERY term inside the bracket. So, 3(x + 2) is (3 * x) + (3 * 2) = 3x + 6.
MISTAKE: Forgetting to carry the sign when multiplying. For example, 5(y - 3) becomes 5y + 15. | CORRECTION: Always multiply the sign as well. 5(y - 3) means 5 * y and 5 * (-3), which is 5y - 15.
MISTAKE: Getting confused when there's a variable outside the bracket. For example, x(x + 5) becomes x + 5x. | CORRECTION: Treat the variable outside like a number and multiply it by each term. x(x + 5) = (x * x) + (x * 5) = x^2 + 5x.
Practice Questions
Try It Yourself
QUESTION: Expand 6(a + 4). | ANSWER: 6a + 24
QUESTION: Expand 5(2b - 7). | ANSWER: 10b - 35
QUESTION: Expand -2(3c + 5). | ANSWER: -6c - 10
MCQ
Quick Quiz
Which of these is the correct expansion of 7(p - 8)?
7p + 8
7p - 56
7p - 8
p - 56
The Correct Answer Is:
B
To expand 7(p - 8), you multiply 7 by p to get 7p, and then you multiply 7 by -8 to get -56. So the correct answer is 7p - 56.
Real World Connection
In the Real World
When you budget for a family trip, say 4 people are going, and each person needs (Rs 500 for food + Rs 300 for travel). You can calculate total cost as 4 * (500 + 300) = (4 * 500) + (4 * 300). This is exactly expanding a bracket to find the total expense for food and travel separately.
Key Vocabulary
Key Terms
EXPAND: To remove brackets by multiplying each term inside by the term outside. | BRACKET: A symbol (like ( )) used to group terms. | TERM: A single number, variable, or product of numbers and variables. | DISTRIBUTE: To multiply the outside term by every term inside the bracket.
What's Next
What to Learn Next
Great job understanding how to expand simple brackets! Next, you can learn about 'Factoring Expressions', which is the opposite of expanding. It's like putting the numbers back into brackets, and it's super useful for solving equations!
