Multiplying the Expressions

Oct 13, 2025 by windailys.com 32 views

Introduction

Multiplying algebraic expressions is a fundamental concept in mathematics that involves combining like terms and applying the distributive property. In this article, we will focus on multiplying two binomial expressions, ${(x+7)}$ and ${(3x-2)}$ , and explore the different methods to achieve this.

The Distributive Property

The distributive property is a fundamental concept in algebra that states that for any real numbers ${a}$ , ${b}$ , and ${c}$ , the following equation holds:

${a(b+c) = ab + ac}$

This property can be applied to multiply two binomial expressions by multiplying each term in the first expression by each term in the second expression.

Multiplying the Expressions

To multiply the expressions ${(x+7)}$ and ${(3x-2)}$ , we will apply the distributive property. We will multiply each term in the first expression by each term in the second expression and then combine like terms.

${(x+7)(3x-2) = x(3x-2) + 7(3x-2)}$

Expanding the Terms

Now, we will expand the terms by multiplying each term in the first expression by each term in the second expression.

${x(3x-2) = 3x^2 - 2x}$

${7(3x-2) = 21x - 14}$

Combining Like Terms

Now, we will combine like terms by adding or subtracting the coefficients of the same variables.

${3x^2 - 2x + 21x - 14 = 3x^2 + 19x - 14}$

Conclusion

In conclusion, multiplying the expressions ${(x+7)}$ and ${(3x-2)}$ using the distributive property and combining like terms results in the expression ${3x^2 + 19x - 14}$ . This is the correct answer among the options provided.

Answer

The correct answer is:

B. ${ $3x^2 + 19x - 14\$}$

Tips and Tricks

When multiplying algebraic expressions, always apply the distributive property to each term in the first expression.
Combine like terms by adding or subtracting the coefficients of the same variables.
Use the distributive property to multiply binomial expressions.

Common Mistakes

Failing to apply the distributive property to each term in the first expression.
Not combining like terms correctly.
Not using the distributive property to multiply binomial expressions.

Real-World Applications

Multiplying algebraic expressions has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, the concept of multiplying algebraic expressions is used to describe the motion of objects under the influence of forces. In engineering, the concept of multiplying algebraic expressions is used to design and optimize systems. In economics, the concept of multiplying algebraic expressions is used to model and analyze economic systems.

Conclusion

Introduction

Multiplying algebraic expressions is a fundamental concept in mathematics that involves combining like terms and applying the distributive property. In this article, we will provide a Q&A guide to help you understand the concept of multiplying algebraic expressions and apply it to real-world problems.

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that states that for any real numbers ${a}$ , ${b}$ , and ${c}$ , the following equation holds:

${a(b+c) = ab + ac}$

This property can be applied to multiply two binomial expressions by multiplying each term in the first expression by each term in the second expression.

Q: How do I multiply two binomial expressions?

A: To multiply two binomial expressions, you will apply the distributive property. You will multiply each term in the first expression by each term in the second expression and then combine like terms.

Q: What is the correct order of operations when multiplying algebraic expressions?

A: The correct order of operations when multiplying algebraic expressions is:

Multiply each term in the first expression by each term in the second expression.
Combine like terms by adding or subtracting the coefficients of the same variables.

Q: How do I combine like terms?

A: To combine like terms, you will add or subtract the coefficients of the same variables. For example, if you have the expression ${3x^2 + 2x + 7x - 4}$ , you will combine the like terms ${2x}$ and ${7x}$ to get ${9x}$ .

Q: What are some common mistakes to avoid when multiplying algebraic expressions?

A: Some common mistakes to avoid when multiplying algebraic expressions include:

Failing to apply the distributive property to each term in the first expression.
Not combining like terms correctly.
Not using the distributive property to multiply binomial expressions.

Q: How do I apply the concept of multiplying algebraic expressions to real-world problems?

A: The concept of multiplying algebraic expressions has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, the concept of multiplying algebraic expressions is used to describe the motion of objects under the influence of forces. In engineering, the concept of multiplying algebraic expressions is used to design and optimize systems. In economics, the concept of multiplying algebraic expressions is used to model and analyze economic systems.

Q: What are some tips and tricks for multiplying algebraic expressions?

A: Some tips and tricks for multiplying algebraic expressions include:

Always apply the distributive property to each term in the first expression.
Combine like terms by adding or subtracting the coefficients of the same variables.
Use the distributive property to multiply binomial expressions.

Conclusion

In conclusion, multiplying algebraic expressions is a fundamental concept in mathematics that involves combining like terms and applying the distributive property. By following the steps outlined in this article and avoiding common mistakes, you can multiply algebraic expressions with ease and apply the concept to real-world problems.

Frequently Asked Questions

Q: What is the distributive property? A: The distributive property is a fundamental concept in algebra that states that for any real numbers ${a}$ , ${b}$ , and ${c}$ , the following equation holds: ${a(b+c) = ab + ac}$
Q: How do I multiply two binomial expressions? A: To multiply two binomial expressions, you will apply the distributive property. You will multiply each term in the first expression by each term in the second expression and then combine like terms.
Q: What is the correct order of operations when multiplying algebraic expressions? A: The correct order of operations when multiplying algebraic expressions is:
1. Multiply each term in the first expression by each term in the second expression.
2. Combine like terms by adding or subtracting the coefficients of the same variables.

Common Mistakes

Failing to apply the distributive property to each term in the first expression.
Not combining like terms correctly.
Not using the distributive property to multiply binomial expressions.

Real-World Applications

The concept of multiplying algebraic expressions has numerous real-world applications in fields such as physics, engineering, and economics.
In physics, the concept of multiplying algebraic expressions is used to describe the motion of objects under the influence of forces.
In engineering, the concept of multiplying algebraic expressions is used to design and optimize systems.
In economics, the concept of multiplying algebraic expressions is used to model and analyze economic systems.