Simplify the Expression: a + 3(4a-6) Using Distribution

Q: Why do I need to distribute to both terms in the parentheses?

The distributive property requires you to multiply the outside number by every term inside. Think of it like giving out candy - if you have 3 bags for each person, everyone gets 3 bags, not just some people!

Q: How do I handle the negative sign when distributing?

Be extra careful with signs! When you multiply $ 3 \times (-6) $, you get -18, not +18. Remember: positive times negative equals negative.

Q: What does 'combine like terms' mean?

Like terms have the same variable part. Here, $ a $ and $ 12a $ are like terms because they both have the variable a. Add their coefficients: 1 + 12 = 13.

Q: Can I distribute in a different order?

The order of distribution doesn't matter due to the commutative property, but it's clearest to go left to right: first $ 3 \times 4a $, then $ 3 \times (-6) $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:04 Open parentheses properly

00:08 Make sure the outer term multiplies each of the terms

00:19 Calculate the multiplications

00:27 Collect like terms

00:33 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$a+3(4a-6)=$

2

Step-by-step solution

To solve the problem of simplifying the expression $a+3(4a-6)$ , follow these detailed steps:

Step 1: Distribute 3 across the terms in the parentheses.
This means multiplying 3 with each term inside: $4a$ and $-6$ .
Step 2: Perform the multiplication:
$3 \times 4a = 12a$
$3 \times (-6) = -18$
Step 3: Combine the distributed terms with $a$ :
Start with the given expression, $a + 12a - 18$ .
Step 4: Simplify by combining like terms:
Add the coefficients of $a$ : $a + 12a = 13a$ .
Step 5: Form the final expression:
The simplified expression is $13a - 18$ .

Therefore, the solution to the problem is $13a - 18$ , which corresponds to choice 2.

3

Final Answer

$13a-18$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Multiply outside term by each term inside parentheses
Technique: $3(4a-6) = 3 \times 4a + 3 \times (-6) = 12a - 18$
Check: Combine like terms: $a + 12a = 13a$ , final answer $13a - 18$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to both terms
Don't just multiply 3 × 4a = 12a and ignore the -6! This gives you a + 12a instead of a + 12a - 18, leading to 13a instead of 13a - 18. Always multiply the outside term by every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

FAQ

Everything you need to know about this question

Why do I need to distribute to both terms in the parentheses?

+

The distributive property requires you to multiply the outside number by every term inside. Think of it like giving out candy - if you have 3 bags for each person, everyone gets 3 bags, not just some people!

How do I handle the negative sign when distributing?

+

Be extra careful with signs! When you multiply $3 \times (-6)$ , you get -18, not +18. Remember: positive times negative equals negative.

What does 'combine like terms' mean?

+

Like terms have the same variable part. Here, $a$ and $12a$ are like terms because they both have the variable a. Add their coefficients: 1 + 12 = 13.

Can I distribute in a different order?

+

The order of distribution doesn't matter due to the commutative property, but it's clearest to go left to right: first $3 \times 4a$ , then $3 \times (-6)$ .

How can I check if my final answer is correct?

+

Substitute a simple value for a (like a = 1) into both the original expression and your answer. If $1 + 3(4 \times 1 - 6) = 13 \times 1 - 18$ , then both equal -5, so you're right!

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Simplify the Expression: a + 3(4a-6) Using Distribution

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to distribute to both terms in the parentheses?

How do I handle the negative sign when distributing?

What does 'combine like terms' mean?

Can I distribute in a different order?

How can I check if my final answer is correct?

🌟 Unlock Your Math Potential

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