Simplify 2a(b+3)+4(b+3): Finding Equivalent Expressions

Q: How do I spot a common factor quickly?

Look for identical expressions in parentheses or as standalone terms. In $ 2a(b+3) + 4(b+3) $, both terms contain (b+3), so that's your common factor!

Q: What if the numbers in front are different like 2a and 4?

That's fine! The coefficients don't need to match - only the expression in parentheses. You factor out the common binomial and keep the different coefficients: $ (b+3)(2a + 4) $.

Q: Can I simplify (2a + 4) further?

Yes! You can factor out 2 to get $ 2(a + 2) $, making the complete answer $ 2(b+3)(a+2) $. But $ (b+3)(2a+4) $ is also correct!

Q: How do I check if my factoring is right?

Expand your answer using the distributive property. If you get back to the original expression, you're correct! For example: $ (b+3)(2a+4) = 2a(b+3) + 4(b+3) $ ✓

Q: What if I don't see a common factor at first?

Look more carefully! Sometimes factors are rearranged like (3+b) vs (b+3) - these are the same! Also check if you can factor out numbers first, then look for binomial patterns.

Factoring Expressions with Common Binomial Factors

Which of the expressions is equivalent to the expression?

$2a(b+3)+4(b+3)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Factor out a common factor

00:06 Mark the common factors

00:13 Take out the common factors from the parentheses

00:19 Take out the common factors from the parentheses

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which of the expressions is equivalent to the expression?

$2a(b+3)+4(b+3)$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the common factor in the expression.
Step 2: Factor out the common factor using the distributive property.
Step 3: Simplify the expression inside the parentheses.

Now, let's work through each step:

Step 1: Identify the common factor. The given expression is $2a(b+3) + 4(b+3)$ . Notice that both terms have a common factor, which is $(b+3)$ .

Step 2: Factor out the common factor. Using the distributive property in reverse, we can factor out $(b+3)$ :

2a(b+3) + 4(b+3) = (b+3)(2a + 4)

Step 3: Simplify the expression inside the parentheses if needed. In this case, $2a + 4$ is already simplified.

Therefore, the expression $2a(b+3) + 4(b+3)$ simplifies to the equivalent expression $(b+3)(2a+4)$ .

The correct choice that corresponds to this expression is choice 3: $(b+3)(2a+4)$ .

Final Answer

$(b+3)(2a+4)$

Key Points to Remember

Essential concepts to master this topic

Recognition: Look for identical factors like (b+3) in multiple terms
Technique: Factor out common binomial: 2a(b+3) + 4(b+3) = (b+3)(2a+4)
Check: Expand your factored form to verify it equals the original ✓

Common Mistakes

Avoid these frequent errors

Distributing instead of factoring
Don't expand 2a(b+3) to get 2ab + 6a and then try to factor = complicated mess! This makes the problem much harder than needed. Always look for common factors first before expanding anything.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 4x^2 + 6x $$

FAQ

Everything you need to know about this question

How do I spot a common factor quickly?

Look for identical expressions in parentheses or as standalone terms. In $2a(b+3) + 4(b+3)$ , both terms contain (b+3), so that's your common factor!

What if the numbers in front are different like 2a and 4?

That's fine! The coefficients don't need to match - only the expression in parentheses. You factor out the common binomial and keep the different coefficients: $(b+3)(2a + 4)$ .

Can I simplify (2a + 4) further?

Yes! You can factor out 2 to get $2(a + 2)$ , making the complete answer $2(b+3)(a+2)$ . But $(b+3)(2a+4)$ is also correct!

How do I check if my factoring is right?

Expand your answer using the distributive property. If you get back to the original expression, you're correct! For example: $(b+3)(2a+4) = 2a(b+3) + 4(b+3)$ ✓

What if I don't see a common factor at first?

Look more carefully! Sometimes factors are rearranged like (3+b) vs (b+3) - these are the same! Also check if you can factor out numbers first, then look for binomial patterns.

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