Find the Common Factor in 7a+14b: Step-by-Step Solution

Q: How do I know I factored correctly?

Use the distributive property to expand your answer back. If $ 7(a+2b) = 7a + 14b $ matches the original expression, you're correct!

Q: Can I factor out variables too?

Only if every term contains that variable. In $ 7a+14b $, we can't factor out 'a' because the second term has 'b', not 'a'.

Factoring Expressions with Greatest Common Factor

Find the common factor:

$7a+14b$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find a common factor

00:07 Factor 14 into factors 2 and 7

00:11 Mark the common factors

00:19 Take out the common factors from the parentheses

00:29 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

Find the common factor:

$7a+14b$

Step-by-step solution

We divide 14 into a multiplication exercise to help us simplify the calculation accordingly: $7\times a+7\times b\times2=$

We then extract the common factor 7:

$7(a+2\times b)=7(a+2b)$

Final Answer

$7(a+2b)$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the largest number that divides all terms evenly
Technique: Factor out 7 from $7a+14b$ since 7 divides both terms
Check: Expand $7(a+2b) = 7a + 14b$ to verify original expression ✓

Common Mistakes

Avoid these frequent errors

Factoring out only part of the common factor
Don't factor out just any common number like 2 from $7a+14b$ = $2(3.5a+7b)$ ! This creates decimals or leaves more factors inside. Always find the greatest common factor first, which is 7 in this case.

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 find the greatest common factor of the coefficients?

Look at the numbers in front of the variables: 7 and 14. Find the largest number that divides both evenly. Since 7 divides into 7 once and into 14 twice, the GCF is 7.

What if the variables are different like in 7a + 14b?

When variables are different (a and b), you can only factor out the numerical coefficients. The variables stay separate inside the parentheses as (a + 2b).

How do I know I factored correctly?

Use the distributive property to expand your answer back. If $7(a+2b) = 7a + 14b$ matches the original expression, you're correct!

What if there's no common factor?

Every expression has at least the common factor of 1. But if no number greater than 1 divides all terms evenly, then the expression is already in simplest form.

Can I factor out variables too?

Only if every term contains that variable. In $7a+14b$ , we can't factor out 'a' because the second term has 'b', not 'a'.

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