Expand the Expression: Simplifying (y×x)² Step-by-Step

Q: Why do I need to square both y and x separately?

The power of a product rule says that when you raise a product to a power, you must apply that power to each factor. Think of it as: $ (y \times x)^2 = (y \times x)(y \times x) = y^2x^2 $.

Q: What's the difference between (yx)² and y²x?

$ (yx)^2 = y^2x^2 $ means both variables are squared, while $ y^2x $ means only y is squared. The parentheses make a huge difference!

Q: Does the order of variables matter in the answer?

No! $ y^2x^2 $ and $ x^2y^2 $ are exactly the same due to the commutative property of multiplication. You can write the variables in any order.

Q: How do I remember this rule?

Think of it as "sharing the power" - when you have $ (ab)^n $, the exponent n gets shared with both a and b, giving you $ a^n b^n $.

Q: What if there were three variables like (xyz)²?

Same rule applies! $ (xyz)^2 = x^2y^2z^2 $. No matter how many factors you have in the parentheses, each one gets the exponent.

Power Rules with Product Expressions

Insert the corresponding expression:

$\left(y\times x\right)^2=$

❤️ 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 Simplify the following problem

00:03 In order to open parentheses with a multiplication operation and an outside exponent

00:06 We'll raise each factor to the power

00:10 We'll apply this formula to our exercise

00:16 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Insert the corresponding expression:

$\left(y\times x\right)^2=$

Step-by-step solution

To solve this problem, we will apply the power of a product rule to the expression $(y \times x)^2$ .

The power of a product rule states:

$(a \times b)^n = a^n \times b^n$

In this case, the product is $y \times x$ , and the power is 2. Applying the power of a product rule gives us:

$(y \times x)^2 = y^2 \times x^2$

Therefore, the expanded form of the given expression is $\mathbf{y^2 \times x^2}$ .

Final Answer

$y^2\times x^2$

Key Points to Remember

Essential concepts to master this topic

Power of Product Rule: When raising a product to a power, distribute the exponent to each factor
Technique: $(y \times x)^2 = y^2 \times x^2$ means square both variables separately
Check: Verify by expanding: $(y \times x)(y \times x) = y^2x^2$ ✓

Common Mistakes

Avoid these frequent errors

Adding the exponent instead of applying it to each factor
Don't write $(y \times x)^2 = y \times x \times 2$ = multiplication by 2! This treats the exponent as a multiplier instead of a power. Always apply the exponent to each factor separately: $(y \times x)^2 = y^2 \times x^2$ .

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to square both y and x separately?

The power of a product rule says that when you raise a product to a power, you must apply that power to each factor. Think of it as: $(y \times x)^2 = (y \times x)(y \times x) = y^2x^2$ .

What's the difference between (yx)² and y²x?

$(yx)^2 = y^2x^2$ means both variables are squared, while $y^2x$ means only y is squared. The parentheses make a huge difference!

Does the order of variables matter in the answer?

No! $y^2x^2$ and $x^2y^2$ are exactly the same due to the commutative property of multiplication. You can write the variables in any order.

How do I remember this rule?

Think of it as "sharing the power" - when you have $(ab)^n$ , the exponent n gets shared with both a and b, giving you $a^n b^n$ .

What if there were three variables like (xyz)²?

Same rule applies! $(xyz)^2 = x^2y^2z^2$ . No matter how many factors you have in the parentheses, each one gets the exponent.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Exponents Rules 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