Factorise the Expression: Finding Common Factors in 20ab-4ac

Q: How do I find the greatest common factor?

Look at coefficients and variables separately. For 20ab and 4ac: coefficients 20 and 4 have GCF of 4, variables a and b vs. a and c share only a. So GCF is 4a.

Q: What if I can't see the common factors right away?

Break down each term completely! Write $ 20ab = 4 \times 5 \times a \times b $ and $ 4ac = 4 \times a \times c $. Now you can clearly see what's common.

Q: Can I factor this expression differently?

The GCF method gives you the most simplified form. Other factorizations like $ 2(10ab-2ac) $ are correct but not fully factored since you can still factor out more.

Q: How do I check my factorization is correct?

Use the distributive property to expand your answer. $ 4a(5b-c) = 4a \times 5b - 4a \times c = 20ab - 4ac $. If you get the original expression, you're right!

Q: What if there's no common factor?

If terms share no common factors, the expression is already in simplest form. But always double-check by listing all factors of each term first.

Factorization with Greatest Common Factor

Factorise:

$20ab-4ac$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find a common factor

00:04 Factor 20 into factors 4 and 5

00:13 Mark the common factors

00:22 Take out the common factors from the parentheses

00:33 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:

$20ab-4ac$

Step-by-step solution

We first break down the coefficient of 20 into a multiplication exercise. That will help us to simplify the calculation : $5\times4\times a\times b-4\times a\times c$

We then extract 4a as a common factor: $4a(5\times b-c)=4a(5b-c)$

Final Answer

$4a(5b-c)$

Key Points to Remember

Essential concepts to master this topic

Rule: Identify all common factors in both terms first
Technique: Factor out GCF 4a from $20ab-4ac$
Check: Expand $4a(5b-c) = 20ab-4ac$ ✓

Common Mistakes

Avoid these frequent errors

Only factoring out partial common factors
Don't just factor out 4 and ignore the common variable a = $4(5ab-ac)$ ! This misses part of the GCF and leaves the expression incompletely factored. Always identify ALL common factors including variables 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 find the greatest common factor?

Look at coefficients and variables separately. For 20ab and 4ac: coefficients 20 and 4 have GCF of 4, variables a and b vs. a and c share only a. So GCF is 4a.

What if I can't see the common factors right away?

Break down each term completely! Write $20ab = 4 \times 5 \times a \times b$ and $4ac = 4 \times a \times c$ . Now you can clearly see what's common.

Can I factor this expression differently?

The GCF method gives you the most simplified form. Other factorizations like $2(10ab-2ac)$ are correct but not fully factored since you can still factor out more.

How do I check my factorization is correct?

Use the distributive property to expand your answer. $4a(5b-c) = 4a \times 5b - 4a \times c = 20ab - 4ac$ . If you get the original expression, you're right!

What if there's no common factor?

If terms share no common factors, the expression is already in simplest form. But always double-check by listing all factors of each term first.

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