Multiply { (3x + 5)^2$}$.A. ${ 9x^2 + 30x + 25\$} B. ${ 9x^2 + 15x + 25\$} C. ${ 9x^2 - 30x + 25\$} D. ${ 9x^2 + 25\$}

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Introduction

In algebra, the process of multiplying a binomial by itself is known as squaring a binomial. This process is essential in various mathematical operations, including factoring and solving quadratic equations. In this article, we will focus on multiplying the binomial $(3x + 5)^2$ and explore the different methods to achieve this.

Understanding the Problem

To multiply $(3x + 5)^2$, we need to apply the formula for squaring a binomial, which is:

$(a + b)^2 = a^2 + 2ab + b^2$

In this case, $a = 3x$ and $b = 5$. We will use this formula to expand the expression and simplify it.

Step 1: Apply the Formula

Using the formula for squaring a binomial, we can write:

$(3x + 5)^2 = (3x)^2 + 2(3x)(5) + 5^2$

Step 2: Simplify the Expression

Now, we will simplify the expression by evaluating the terms:

$(3x)^2 = 9x^2$

$2(3x)(5) = 30x$

$5^2 = 25$

Step 3: Combine the Terms

Finally, we will combine the terms to get the final result:

$(3x + 5)^2 = 9x^2 + 30x + 25$

Conclusion

In this article, we have demonstrated how to multiply the binomial $(3x + 5)^2$ using the formula for squaring a binomial. We have also simplified the expression and combined the terms to get the final result. The correct answer is:

$9x^2 + 30x + 25$

This result is consistent with the formula for squaring a binomial, which is:

$(a + b)^2 = a^2 + 2ab + b^2$

In this case, $a = 3x$ and $b = 5$, so the correct answer is indeed $9x^2 + 30x + 25$.

Comparison with Other Options

Let's compare our result with the other options:

• Option A: $9x^2 + 30x + 25$ (correct)
• Option B: $9x^2 + 15x + 25$ (incorrect)
• Option C: $9x^2 - 30x + 25$ (incorrect)
• Option D: $9x^2 + 25$ (incorrect)

As we can see, only option A is consistent with our result.

Final Answer

The final answer is:

$9x^2 + 30x + 25$

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Introduction

In our previous article, we demonstrated how to multiply the binomial $(3x + 5)^2$ using the formula for squaring a binomial. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the formula for squaring a binomial?

A: The formula for squaring a binomial is:

$(a + b)^2 = a^2 + 2ab + b^2$

Q: How do I apply the formula to multiply $(3x + 5)^2$?

A: To apply the formula, we need to identify the values of $a$ and $b$. In this case, $a = 3x$ and $b = 5$. We will then substitute these values into the formula and simplify the expression.

Q: What is the correct result for multiplying $(3x + 5)^2$?

A: The correct result is:

$(3x + 5)^2 = 9x^2 + 30x + 25$

Q: Why is option B incorrect?

A: Option B is incorrect because it does not follow the formula for squaring a binomial. The correct result should have a term with $2ab$, which is $30x$ in this case.

Q: Why is option C incorrect?

A: Option C is incorrect because it has a negative term with $-30x$, which is not consistent with the formula for squaring a binomial.

Q: Why is option D incorrect?

A: Option D is incorrect because it does not have the term $2ab$, which is $30x$ in this case.

Q: Can I use the FOIL method to multiply $(3x + 5)^2$?

A: Yes, you can use the FOIL method to multiply $(3x + 5)^2$. The FOIL method is a technique for multiplying two binomials by multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms.

Q: How do I use the FOIL method to multiply $(3x + 5)^2$?

A: To use the FOIL method, we need to multiply the first terms, then the outer terms, then the inner terms, and finally the last terms:

$(3x + 5)^2 = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)$

Simplifying the expression, we get:

$(3x + 5)^2 = 9x^2 + 15x + 15x + 25$

Combining like terms, we get:

$(3x + 5)^2 = 9x^2 + 30x + 25$

Conclusion

In this article, we have answered some frequently asked questions related to multiplying $(3x + 5)^2$. We have also demonstrated how to use the FOIL method to multiply this expression. The correct result is:

$9x^2 + 30x + 25$

This result is consistent with the formula for squaring a binomial, which is:

$(a + b)^2 = a^2 + 2ab + b^2$

In this case, $a = 3x$ and $b = 5$, so the correct answer is indeed $9x^2 + 30x + 25$.