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

Question

Insert the corresponding expression:

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

00:00 Simplify the following problem

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

00:07 Raise each factor to the power

00:11 Raise each factor to the power

00:16 This is the solution

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

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

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

Calculating $2^2$ gives:

$2^2 = 4$

So, the expression simplifies to:

$4 \times x^2$

Therefore, the correct expression is $2^2 \times x^2$ .

This corresponds to Choice 2.

$2^2\times x^2$