Find the Common Factor in the Expression ab+bc: Algebraic Factoring

Q: How do I know which variable to factor out?

Look for the variable that appears in every single term. In $ ab + bc $, the variable 'b' appears in both terms, so that's your common factor!

Q: What if multiple variables appear in all terms?

Factor out all common variables! For example, in $ 3xy + 6xy^2 $, you can factor out both the number 3 and variables xy to get $ 3xy(1 + 2y) $.

Q: Can I factor out numbers too?

Yes! Look for the greatest common factor (GCF) of the coefficients. For $ 4ab + 6bc $, factor out 2b to get $ 2b(2a + 3c) $.

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

Use the distributive property to expand your answer. If $ b(a + c) = ab + bc $ matches the original expression, you're right!

Q: What if there's no common factor?

Sometimes expressions like $ ab + cd $ have no common factors. That's okay - just state that the expression cannot be factored further.

Algebraic Factoring with Common Variable Terms

Find the common factor:

$ab+bc$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Take out a common factor

00:05 Mark the common factors

00:09 Extract the common factors from the parentheses

00:19 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:

$ab+bc$

Step-by-step solution

$ab+bc=a\times b+b\times c$

If we consider that b is the common factor, it can be removed from the equation:

$b(ab+bc)=$

We divide by b: $b(\frac{ab}{b}+\frac{bc}{b})=$

$b(a+c)$

Final Answer

$b(a+c)$

Key Points to Remember

Essential concepts to master this topic

Rule: Look for variables that appear in every term
Technique: Factor out b from ab + bc = b(a + c)
Check: Expand b(a + c) = ab + bc to verify ✓

Common Mistakes

Avoid these frequent errors

Factoring out the wrong variable
Don't factor out 'a' from ab + bc = wrong factorization! The variable 'a' only appears in the first term, so you can't factor it out. Always identify the variable that appears in ALL terms before factoring.

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 know which variable to factor out?

Look for the variable that appears in every single term. In $ab + bc$ , the variable 'b' appears in both terms, so that's your common factor!

What if multiple variables appear in all terms?

Factor out all common variables! For example, in $3xy + 6xy^2$ , you can factor out both the number 3 and variables xy to get $3xy(1 + 2y)$ .

Can I factor out numbers too?

Yes! Look for the greatest common factor (GCF) of the coefficients. For $4ab + 6bc$ , factor out 2b to get $2b(2a + 3c)$ .

How do I check if my factoring is correct?

Use the distributive property to expand your answer. If $b(a + c) = ab + bc$ matches the original expression, you're right!

What if there's no common factor?

Sometimes expressions like $ab + cd$ have no common factors. That's okay - just state that the expression cannot be factored further.

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