Simplify the Expression: 2a+3b-6(a-2b) Using Distributive Property

Q: Why does -6 times -2b equal +12b?

Remember the sign rules: negative times negative equals positive! So $ (-6) \times (-2b) = +12b $. The two negative signs cancel out.

Q: How do I know which terms are like terms?

Like terms have the exact same variable part. In this problem, 2a and -6a are like terms (both have 'a'), and 3b and 12b are like terms (both have 'b').

Q: What if I distributed incorrectly?

Check your work by expanding step-by-step: $ -6(a - 2b) $ means $ (-6 \times a) + (-6 \times -2b) = -6a + 12b $. Take your time with the signs!

Q: Can I combine terms in a different order?

Yes! Addition and subtraction are commutative, so you can group like terms however you want. Just make sure you don't change any signs when rearranging.

Q: Why isn't the answer -4a + b?

That's missing the $ +12b $ from distribution! When you combine $ 3b + 12b $, you get $ 15b $, not just $ b $. Always include all terms.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:07 Let's open parentheses properly

00:10 Make sure the outer term multiplies each of the terms

00:22 Let's collect terms

00:37 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

$2a+3b-6(a-2b)=$

2

Step-by-step solution

To solve this problem, we'll apply the distributive property and combine like terms.

Step 1: Apply the distributive property.
We have the expression $2a + 3b - 6(a - 2b)$ . Let's distribute the $-6$ across the terms inside the parentheses:
$-6(a - 2b) = -6 \cdot a + (-6) \cdot (-2b) = -6a + 12b$ .
Step 2: Combine like terms.
Now substitute $-6a + 12b$ back into the expression:
$2a + 3b - 6a + 12b$ .
Combine the like terms, $2a$ and $-6a$ , and $3b$ and $12b$ :
$(2a - 6a) + (3b + 12b) = -4a + 15b$ .

Therefore, the simplified expression is $-4a + 15b$ , which matches choice 2.

3

Final Answer

$-4a+15b$

Key Points to Remember

Essential concepts to master this topic

Distributive Rule: Multiply outside term by each term inside parentheses
Technique: $-6(a - 2b) = -6a + 12b$ using sign rules
Check: Count like terms: 2a terms and 3b terms combine correctly ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the negative sign
Don't just multiply $-6 \times a = -6a$ and forget the second term! This gives $2a + 3b - 6a$ instead of $2a + 3b - 6a + 12b$ . Always distribute to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 3+3+3+3 $$

$3\times4$

FAQ

Everything you need to know about this question

Why does -6 times -2b equal +12b?

+

Remember the sign rules: negative times negative equals positive! So $(-6) \times (-2b) = +12b$ . The two negative signs cancel out.

How do I know which terms are like terms?

+

Like terms have the exact same variable part. In this problem, 2a and -6a are like terms (both have 'a'), and 3b and 12b are like terms (both have 'b').

What if I distributed incorrectly?

+

Check your work by expanding step-by-step: $-6(a - 2b)$ means $(-6 \times a) + (-6 \times -2b) = -6a + 12b$ . Take your time with the signs!

Can I combine terms in a different order?

+

Yes! Addition and subtraction are commutative, so you can group like terms however you want. Just make sure you don't change any signs when rearranging.

Why isn't the answer -4a + b?

+

That's missing the $+12b$ from distribution! When you combine $3b + 12b$ , you get $15b$ , not just $b$ . Always include all terms.

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Simplify the Expression: 2a+3b-6(a-2b) Using Distributive Property

Distributive Property with Negative Multiplication

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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 does -6 times -2b equal +12b?

How do I know which terms are like terms?

What if I distributed incorrectly?

Can I combine terms in a different order?

Why isn't the answer -4a + b?

🌟 Unlock Your Math Potential

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