Finding the Common Factor in 2y + 4: Algebraic Expression Simplification

Q: Why isn't y the common factor?

For a factor to be common, it must appear in every single term. Since y only appears in $ 2y $ but not in 4, it cannot be factored out.

Q: How do I find the greatest common factor quickly?

Look at just the numerical coefficients first. Find the largest number that divides both 2 and 4 evenly. That's your GCF!

Q: What if there were more terms like 2y + 4 + 6?

Find the GCF of all coefficients: 2, 4, and 6. The GCF is still 2, so you'd get $ 2(y + 2 + 3) $.

Q: Can I factor out 4 instead of 2?

No! You can only factor out numbers that divide all terms. Since 4 doesn't divide 2y evenly (2 ÷ 4 = 0.5), it's not a valid common factor.

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

Use the distributive property to expand your factored form. If you get back to the original expression, your factoring is correct!

Factor Identification with Numerical Coefficients

The expression $2y + 4$ is to be simplified by factoring. What is the common factor?

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Step-by-step written solution

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Understand the problem

The expression $2y + 4$ is to be simplified by factoring. What is the common factor?

Step-by-step solution

Consider the expression $2y + 4$ .

Decompose each term into factors:

$2y$ can be rewritten as $2 \cdot y$ .

$4$ can be rewritten as $2 \cdot 2$ .

The common factor of these terms is $2$ .

This means you can factor the expression as $2(y + 2)$ . Therefore, the common factor is $2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the largest number that divides all terms evenly
Technique: Factor each term: $2y = 2 \cdot y$ and $4 = 2 \cdot 2$
Check: Expand $2(y + 2) = 2y + 4$ to verify factoring ✓

Common Mistakes

Avoid these frequent errors

Choosing a variable as the common factor
Don't assume y is the common factor just because it appears in one term = wrong factoring! Variables can't factor out if they're not in every term. Always look for the largest number that divides all coefficients.

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

Why isn't y the common factor?

For a factor to be common, it must appear in every single term. Since y only appears in $2y$ but not in 4, it cannot be factored out.

How do I find the greatest common factor quickly?

Look at just the numerical coefficients first. Find the largest number that divides both 2 and 4 evenly. That's your GCF!

What if there were more terms like 2y + 4 + 6?

Find the GCF of all coefficients: 2, 4, and 6. The GCF is still 2, so you'd get $2(y + 2 + 3)$ .

Can I factor out 4 instead of 2?

No! You can only factor out numbers that divide all terms. Since 4 doesn't divide 2y evenly (2 ÷ 4 = 0.5), it's not a valid common factor.

How do I check if my factoring is correct?

Use the distributive property to expand your factored form. If you get back to the original expression, your factoring is correct!

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