Factorize the Expression: 13abcd + 26ab Step-by-Step

Q: How do I find the GCF when there are both numbers and variables?

Look at numbers separately from variables! For coefficients 13 and 26, the GCF is 13. For variables, find what appears in both terms: both have a and b, so ab is common.

Q: Why isn't 13(abcd + 2ab) the right answer?

Because you can factor out more! The second term 2ab still has ab that can be factored out. The complete factorization is $ 13ab(cd + 2) $.

Q: How do I check my factorization is correct?

Distribute back! Multiply $ 13ab(cd + 2) $ to get $ 13abcd + 26ab $. If it matches the original, you're right!

Factorization with Common Variable Terms

Factorise:

$13abcd+26ab$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find a common factor

00:11 Factor 26 into 13 and 2

00:19 Mark the common factors

00:24 Take out the common factors from the parentheses

00:40 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

Factorise:

$13abcd+26ab$

Step-by-step solution

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

Step 1: Identify the greatest common factor (GCF) of the terms in the expression.
Step 2: Factor out the GCF from the expression.
Step 3: Simplify the expression inside the parentheses.

Step 1: Determine the GCF of the terms $13abcd$ and $26ab$ .
The GCF of the coefficients $13$ and $26$ is $13$ .
The variables $a$ and $b$ are common in both terms, so the GCF of the variables is $ab$ .

Therefore, the GCF of the expression is $13ab$ .

Step 2: Factor out the GCF.
Factor $13ab$ from each term in the expression:
$13abcd + 26ab = 13ab(cd) + 13ab(2)$

Step 3: Simplify to obtain the final factorised expression:
$13ab(cd + 2)$

Therefore, the factorised form of the expression is $13ab(cd + 2)$ .

Among the given choices, this corresponds to choice 2: $13ab(cd+2)$ .

Final Answer

$13ab(cd+2)$

Key Points to Remember

Essential concepts to master this topic

GCF Rule: Find common numerical and variable factors together
Factor Method: 13abcd = 13ab(cd) and 26ab = 13ab(2)
Verify: Distribute back: 13ab(cd + 2) = 13abcd + 26ab ✓

Common Mistakes

Avoid these frequent errors

Only factoring out the numerical coefficient
Don't just factor out 13 to get 13(abcd + 2ab) = wrong! This leaves ab unfactored in the second term, making further simplification impossible. Always factor out all common factors including variables like ab.

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 GCF when there are both numbers and variables?

Look at numbers separately from variables! For coefficients 13 and 26, the GCF is 13. For variables, find what appears in both terms: both have a and b, so ab is common.

Why isn't 13(abcd + 2ab) the right answer?

Because you can factor out more! The second term 2ab still has ab that can be factored out. The complete factorization is $13ab(cd + 2)$ .

What if the terms don't seem to have common factors?

Look more carefully! Even if variables seem different, check if some appear in both terms. Here, both 13abcd and 26ab contain the variables a and b.

How do I check my factorization is correct?

Distribute back! Multiply $13ab(cd + 2)$ to get $13abcd + 26ab$ . If it matches the original, you're right!

Can I factor this expression in a different order?

The final answer will be the same! You might factor 13 first, then ab, but you'll still get $13ab(cd + 2)$ . The GCF method is most efficient.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Algebraic Technique questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime