Find The Product. ( 4 X Y ) ( 7 Y (4xy)(7y ( 4 X Y ) ( 7 Y ]

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Introduction

In mathematics, the product of two or more numbers or expressions is a fundamental concept that is used extensively in various branches of mathematics, including algebra, geometry, and calculus. The product of two or more numbers or expressions is obtained by multiplying them together. In this article, we will focus on finding the product of two expressions, $(4xy)$ and $(7y^2)$.

Understanding the Problem

To find the product of $(4xy)$ and $(7y^2)$, we need to multiply these two expressions together. This involves multiplying the coefficients, the variables, and the exponents of the variables. The coefficients are the numerical values that are multiplied together, while the variables are the letters or symbols that are multiplied together. The exponents are the powers to which the variables are raised.

Multiplying the Coefficients

The coefficients of the two expressions are 4 and 7, respectively. To multiply these coefficients, we simply multiply them together.

Multiplying the Coefficients:

4 × 7 = 28

Multiplying the Variables

The variables in the two expressions are x and y. To multiply these variables, we simply multiply them together.

Multiplying the Variables:

x × y = xy

Multiplying the Exponents

The exponents of the variables in the two expressions are 1 and 2, respectively. To multiply these exponents, we add them together.

Multiplying the Exponents:

1 + 2 = 3

Combining the Results

Now that we have multiplied the coefficients, the variables, and the exponents, we can combine the results to find the product of $(4xy)$ and $(7y^2)$.

Combining the Results:

28 × xy × y^3 = 28xy^4

Conclusion

In this article, we have found the product of two expressions, $(4xy)$ and $(7y^2)$. We have multiplied the coefficients, the variables, and the exponents of the variables to obtain the final result. The product of these two expressions is 28xy^4.

Example Problems

Here are a few example problems that involve finding the product of two or more expressions:

• Find the product of $(3x^2)$ and $(4y^3)$.
• Find the product of $(2xy)$ and $(5z^2)$.
• Find the product of $(6x^3)$ and $(9y^2)$.

Solutions to Example Problems

Here are the solutions to the example problems:

• Find the product of $(3x^2)$ and $(4y^3)$:

Multiplying the Coefficients:

3 × 4 = 12

Multiplying the Variables:

x^2 × y^3 = x^2y3

Multiplying the Exponents:

2 + 3 = 5

Combining the Results:

12 × x^2y3 = 12x^2y3

• Find the product of $(2xy)$ and $(5z^2)$:

Multiplying the Coefficients:

2 × 5 = 10

Multiplying the Variables:

x × y × z^2 = xyz^2

Combining the Results:

10 × xyz^2 = 10xyz^2

• Find the product of $(6x^3)$ and $(9y^2)$:

Multiplying the Coefficients:

6 × 9 = 54

Multiplying the Variables:

x^3 × y^2 = x^3y2

Multiplying the Exponents:

3 + 2 = 5

Combining the Results:

54 × x^3y2 = 54x^3y2

Tips and Tricks

Here are a few tips and tricks that can help you find the product of two or more expressions:

• Make sure to multiply the coefficients, the variables, and the exponents of the variables.
• Use the distributive property to multiply the variables.
• Use the exponent rule to multiply the exponents.
• Simplify the expression by combining like terms.

Conclusion

In this article, we have found the product of two expressions, $(4xy)$ and $(7y^2)$. We have multiplied the coefficients, the variables, and the exponents of the variables to obtain the final result. The product of these two expressions is 28xy^4. We have also provided example problems and solutions to help you practice finding the product of two or more expressions.

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Introduction

In our previous article, we found the product of two expressions, $(4xy)$ and $(7y^2)$. We multiplied the coefficients, the variables, and the exponents of the variables to obtain the final result. The product of these two expressions is 28xy^4. In this article, we will answer some frequently asked questions about finding the product of two or more expressions.

Q&A

Q: What is the product of $(3x^2)$ and $(4y^3)$?

A: To find the product of $(3x^2)$ and $(4y^3)$, we multiply the coefficients, the variables, and the exponents of the variables. The product is 12x^2y3.

Q: How do I find the product of $(2xy)$ and $(5z^2)$?

A: To find the product of $(2xy)$ and $(5z^2)$, we multiply the coefficients, the variables, and the exponents of the variables. The product is 10xyz^2.

Q: What is the product of $(6x^3)$ and $(9y^2)$?

A: To find the product of $(6x^3)$ and $(9y^2)$, we multiply the coefficients, the variables, and the exponents of the variables. The product is 54x^3y2.

Q: How do I multiply the coefficients of two expressions?

A: To multiply the coefficients of two expressions, we simply multiply them together. For example, if we have the expressions $(3x^2)$ and $(4y^3)$, we multiply the coefficients 3 and 4 to get 12.

Q: How do I multiply the variables of two expressions?

A: To multiply the variables of two expressions, we simply multiply them together. For example, if we have the expressions $(2xy)$ and $(5z^2)$, we multiply the variables x and y to get xy, and then multiply xy by z^2 to get xyz^2.

Q: How do I multiply the exponents of two expressions?

A: To multiply the exponents of two expressions, we add them together. For example, if we have the expressions $(3x^2)$ and $(4y^3)$, we add the exponents 2 and 3 to get 5.

Q: What is the distributive property?

A: The distributive property is a rule that allows us to multiply a single term by two or more terms. For example, if we have the expression $(3x^2)$ and we want to multiply it by $(4y^3)$, we can use the distributive property to get 12x^2y3.

Q: What is the exponent rule?

A: The exponent rule is a rule that allows us to multiply the exponents of two expressions. For example, if we have the expressions $(3x^2)$ and $(4y^3)$, we can use the exponent rule to add the exponents 2 and 3 to get 5.

Q: How do I simplify an expression?

A: To simplify an expression, we combine like terms. For example, if we have the expression 12x^2y3 + 10x^2y3, we can combine the like terms to get 22x^2y3.

Conclusion

In this article, we have answered some frequently asked questions about finding the product of two or more expressions. We have also provided examples and explanations to help you understand the concepts. Remember to multiply the coefficients, the variables, and the exponents of the variables, and to use the distributive property and the exponent rule to simplify the expression.

Tips and Tricks

Here are a few tips and tricks that can help you find the product of two or more expressions:

• Make sure to multiply the coefficients, the variables, and the exponents of the variables.
• Use the distributive property to multiply the variables.
• Use the exponent rule to multiply the exponents.
• Simplify the expression by combining like terms.
• Practice, practice, practice!

Example Problems

Here are a few example problems that involve finding the product of two or more expressions:

• Find the product of $(3x^2)$ and $(4y^3)$.
• Find the product of $(2xy)$ and $(5z^2)$.
• Find the product of $(6x^3)$ and $(9y^2)$.

Solutions to Example Problems

Here are the solutions to the example problems:

• Find the product of $(3x^2)$ and $(4y^3)$:

Multiplying the Coefficients:

3 × 4 = 12

Multiplying the Variables:

x^2 × y^3 = x^2y3

Multiplying the Exponents:

2 + 3 = 5

Combining the Results:

12 × x^2y3 = 12x^2y3

• Find the product of $(2xy)$ and $(5z^2)$:

Multiplying the Coefficients:

2 × 5 = 10

Multiplying the Variables:

x × y × z^2 = xyz^2

Combining the Results:

10 × xyz^2 = 10xyz^2

• Find the product of $(6x^3)$ and $(9y^2)$:

Multiplying the Coefficients:

6 × 9 = 54

Multiplying the Variables:

x^3 × y^2 = x^3y2

Multiplying the Exponents:

3 + 2 = 5

Combining the Results:

54 × x^3y2 = 54x^3y2