Finding the Common Factor in 25y-100xy²: Algebraic Expression Analysis

Q: How do I find the greatest common factor of two terms?

Look at both the coefficients and the variables separately. For 25y and 100xy², the GCF of coefficients is 25, and the GCF of variables is y. So the overall GCF is $ 25y $.

Q: What if I only factor out y instead of 25y?

You'd get $ y(25 - 100xy) $, but this isn't fully factored! You can still factor out 25 from the parentheses: $ y \cdot 25(1 - 4xy) = 25y(1 - 4xy) $.

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

Always distribute back! Multiply your factored form: $ 25y \times 1 + 25y \times (-4xy) = 25y - 100xy^2 $. If you get the original expression, you're right!

Q: Why is the x not part of the common factor?

Because x doesn't appear in every term. The first term is $ 25y $ with no x, so x cannot be factored out of the entire expression.

Factoring Algebraic Expressions with Common Terms

Find the common factor:

$25y-100xy^2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Take out common factor

00:04 Break down 100 into factors 25 and 4

00:13 Mark the common factors

00:23 Extract the common factors from the parentheses

00:32 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:

$25y-100xy^2$

Step-by-step solution

First, we will decompose the coefficients of the multiplication exercise that will help us find the common factor:

$25\times y-4\times25\times x\times y\times y$

Now find the common factor 25y:

$25y(1-4xy)$

Final Answer

$25y(1-4xy)$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of all terms first
Technique: Factor out 25y from both terms: $25y \cdot 1 - 25y \cdot 4xy$
Check: Distribute back: $25y(1-4xy) = 25y - 100xy^2$ ✓

Common Mistakes

Avoid these frequent errors

Factoring out only part of the common factor
Don't factor out just 25 or just y and leave the rest = incomplete factoring! This doesn't fully simplify the expression and makes it harder to work with. Always find the greatest common factor of ALL terms, which here is 25y.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 2x^2 $$

FAQ

Everything you need to know about this question

How do I find the greatest common factor of two terms?

Look at both the coefficients and the variables separately. For 25y and 100xy², the GCF of coefficients is 25, and the GCF of variables is y. So the overall GCF is $25y$ .

Why can't I factor out 4 like in answer choice B?

While 4 divides into 100, it doesn't divide evenly into 25. The first term $25y$ would become $\frac{25y}{4}$ , which creates fractions unnecessarily.

What if I only factor out y instead of 25y?

You'd get $y(25 - 100xy)$ , but this isn't fully factored! You can still factor out 25 from the parentheses: $y \cdot 25(1 - 4xy) = 25y(1 - 4xy)$ .

How do I check if my factoring is correct?

Always distribute back! Multiply your factored form: $25y \times 1 + 25y \times (-4xy) = 25y - 100xy^2$ . If you get the original expression, you're right!

Why is the x not part of the common factor?

Because x doesn't appear in every term. The first term is $25y$ with no x, so x cannot be factored out of the entire expression.

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