Simplify The Expression: \[$(4gz)^2\$\]

**Simplify the Expression: $(4gz)^2$** =====================================

What is the Simplified Form of the Expression?

The given expression is $(4gz)^2$. To simplify this expression, we need to expand it using the formula $(ab)^2 = a^2b^2$. Let's break it down step by step.

Step 1: Expand the Expression

Using the formula $(ab)^2 = a^2b^2$, we can expand the given expression as follows:

$(4gz)^2 = (4g)^2(z)^2$

Step 2: Simplify the Expression

Now, let's simplify the expression further by squaring the terms inside the parentheses:

$(4g)^2 = 16g^2$

$(z)^2 = z^2$

So, the simplified form of the expression is:

$16g^2z^2$

Q&A Session

Q: What is the formula to expand the expression $(ab)^2$? A: The formula to expand the expression $(ab)^2$ is $a^2b^2$.

Q: How do I simplify the expression $(4gz)^2$? A: To simplify the expression $(4gz)^2$, you need to expand it using the formula $(ab)^2 = a^2b^2$. Then, simplify the expression further by squaring the terms inside the parentheses.

Q: What is the simplified form of the expression $(4gz)^2$? A: The simplified form of the expression $(4gz)^2$ is $16g^2z^2$.

Q: Can I use the distributive property to simplify the expression $(4gz)^2$? A: No, you cannot use the distributive property to simplify the expression $(4gz)^2$. The distributive property is used to expand expressions with multiple terms, but in this case, we are dealing with a squared expression.

Q: How do I know when to use the formula $(ab)^2 = a^2b^2$? A: You should use the formula $(ab)^2 = a^2b^2$ when you are dealing with a squared expression that can be expanded using this formula.

Common Mistakes to Avoid

• Not using the correct formula to expand the expression
• Not simplifying the expression further by squaring the terms inside the parentheses
• Using the distributive property to simplify the expression

Conclusion

Simplifying the expression $(4gz)^2$ requires expanding it using the formula $(ab)^2 = a^2b^2$ and then simplifying the expression further by squaring the terms inside the parentheses. By following these steps, you can arrive at the simplified form of the expression, which is $16g^2z^2$. Remember to use the correct formula and simplify the expression carefully to avoid common mistakes.