Expand (2x)² : Converting Product Square to Standard Form

Power of Product with Algebraic Terms

Insert the corresponding expression:

(2×x)2= \left(2\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
00:06 Let's simplify this math problem together.
00:10 To begin, open the parentheses by using multiplication and the outside exponent.
00:15 Raise each part inside the parentheses to the power.
00:19 Make sure every factor is raised to the power.
00:23 And that's how you find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Insert the corresponding expression:

(2×x)2= \left(2\times x\right)^2=

2

Step-by-step solution

To solve the expression (2×x)2(2 \times x)^2, we'll follow these steps:

  • Step 1: Identify the base of the exponent, which is the product 2×x2 \times x.
  • Step 2: Apply the Power of a Product rule, which states that (ab)n=an×bn(ab)^n = a^n \times b^n.
  • Step 3: Distribute the exponent to both factors within the parentheses:

(2×x)2=22×x2(2 \times x)^2 = 2^2 \times x^2

Calculating 222^2 gives:

22=42^2 = 4

So, the expression simplifies to:

4×x24 \times x^2

Therefore, the correct expression is 22×x22^2 \times x^2.

This corresponds to Choice 2.

3

Final Answer

22×x2 2^2\times x^2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Apply exponent to each factor: (ab)n=an×bn (ab)^n = a^n \times b^n
  • Technique: Distribute the squared exponent: (2x)2=22×x2 (2x)^2 = 2^2 \times x^2
  • Check: Verify by calculating: 22×x2=4x2 2^2 \times x^2 = 4x^2 ✓

Common Mistakes

Avoid these frequent errors
  • Only squaring one part of the product
    Don't square just the coefficient or just the variable like 2x2 2x^2 or 4x 4x ! This ignores the power rule and gives incomplete results. Always distribute the exponent to both the coefficient AND the variable when squaring a product.

Practice Quiz

Test your knowledge with interactive questions

\( 112^0=\text{?} \)

FAQ

Everything you need to know about this question

Why can't I just write 2x2 2x^2 ?

+

Because (2x)2 (2x)^2 means both the 2 and the x are squared! The parentheses show that 2x is treated as one unit. If you only square the x, you're missing the 22 2^2 part.

What's the difference between (2x)2 (2x)^2 and 2x2 2x^2 ?

+

(2x)2=4x2 (2x)^2 = 4x^2 because you square everything inside parentheses. But 2x2 2x^2 means only the x is squared, so the 2 stays as 2. Big difference!

Do I always need to show 22×x2 2^2 \times x^2 before simplifying?

+

For learning purposes, yes! Writing 22×x2 2^2 \times x^2 shows you correctly applied the power rule. Once you're confident, you can go straight to 4x2 4x^2 .

What if the coefficient was negative like (−2x)2 (-2x)^2 ?

+

Same rule applies! (−2x)2=(−2)2×x2=4x2 (-2x)^2 = (-2)^2 \times x^2 = 4x^2 . Remember, a negative number squared becomes positive!

How do I remember the power of a product rule?

+

Think of it as: "The exponent visits everyone inside the parentheses!" Each factor gets raised to that power. Use (ab)n=anbn (ab)^n = a^n b^n as your guide.

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations

Power of a Product

Simplify the Expression: Finding (y×3)² Step by Step
Click to solve
Evaluate (a×3)³: Expanding the Cube of a Product
Click to solve