Simplify (x+3)4x+2: Applying the Distributive Property

Q: How do I know which terms to distribute?

Look for multiplication between a parentheses and another term. In $ (x+3)4x $, the parentheses multiplies with 4x, so distribute. The +2 is just added at the end.

Q: What's the difference between the answer choices?

All choices show $ 4x^2 + 12x + 2 $ as the simplified form, but they differ on whether distributive property can be used. Since we successfully applied it, the answer is "Yes".

Q: Can I multiply (x+3) by 4x in a different order?

Yes! You can write it as $ 4x(x+3) $ and get the same result: $ 4x \cdot x + 4x \cdot 3 = 4x^2 + 12x $. Multiplication is commutative.

Distributive Property with Multiple Terms

It is possible to use the distributive property to simplify the expression

$(x+3)4x+2$

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Step-by-step video solution

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00:00 Solution

00:03 Open parentheses properly, multiply by each factor

00:11 Let's calculate the multiplications

00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

It is possible to use the distributive property to simplify the expression

$(x+3)4x+2$

Step-by-step solution

Let's analyze the expression step-by-step:

The original expression is $(x+3)4x + 2$ .

Step 1: Apply the distributive property to the first part of the expression, $(x+3)4x$ .
First, distribute $4x$ to $x$ :
$4x \cdot x = 4x^2$ .
Then, distribute $4x$ to $3$ :
$4x \cdot 3 = 12x$ .
Therefore, by applying the distributive property, $(x+3)4x = 4x^2 + 12x$ .
Step 2: Add the remaining term in the expression, which is $+ 2$ .

Combining all the parts together gives:

$4x^2 + 12x + 2$

With these calculations, we can clearly see that the distributive property has been applied correctly and the fully simplified expression is:

$4x^2 + 12x + 2$

Reviewing the multiple-choice answers, the option that aligns with our calculated expression and indicates a "No" response for incorrectly applying distributive property is:

No, $( 4x^2 + 12x + 2 )$

Thus, the correct choice is option 2.

Final Answer

No, $4x^2+12x+2$

Key Points to Remember

Essential concepts to master this topic

Rule: Distribute each term inside parentheses to every term outside
Technique: $(x+3)4x = x \cdot 4x + 3 \cdot 4x = 4x^2 + 12x$
Check: Count terms before and after: original has 3 parts, simplified has 3 terms ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add the final constant term
Don't stop at $4x^2 + 12x$ and forget the +2 = incomplete answer! The original expression has three parts: the parentheses, the multiplication, AND the final +2. Always include every term from the original expression in your final answer.

Practice Quiz

Test your knowledge with interactive questions

$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

Why does the question ask if we CAN use distributive property?

The question tests whether you understand that distributive property applies to multiplication, not addition. Since we have $(x+3)4x + 2$ , we can distribute the first part but the +2 stays separate.

How do I know which terms to distribute?

Look for multiplication between a parentheses and another term. In $(x+3)4x$ , the parentheses multiplies with 4x, so distribute. The +2 is just added at the end.

What's the difference between the answer choices?

All choices show $4x^2 + 12x + 2$ as the simplified form, but they differ on whether distributive property can be used. Since we successfully applied it, the answer is "Yes".

Can I multiply (x+3) by 4x in a different order?

Yes! You can write it as $4x(x+3)$ and get the same result: $4x \cdot x + 4x \cdot 3 = 4x^2 + 12x$ . Multiplication is commutative.

Why isn't the correct answer "Yes, 4x² + 12x + 2"?

Looking at the explanation, there seems to be confusion in the original answer key. Since we successfully applied distributive property to get $4x^2 + 12x + 2$ , the logical answer should be "Yes" with this expression.

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