Multiplying the Given Expression

Oct 13, 2025 by windailys.com 97 views

Introduction

In algebra, multiplying and simplifying expressions is a crucial skill that helps us solve equations and inequalities. In this article, we will focus on multiplying and simplifying the expression ${$ (3 - 4x)(3 - 8x)$}$. We will break down the process into manageable steps, making it easier to understand and apply.

What is Multiplication in Algebra?

In algebra, multiplication is a way of combining two or more expressions to form a new expression. When we multiply two expressions, we are essentially adding or subtracting the same value multiple times. For example, ${$ (2x)(3x)$}$ is equivalent to ${ $2x + 2x + 2x + 2x\$}$ .

Multiplying the Given Expression

To multiply the given expression ${$ (3 - 4x)(3 - 8x)$}$, we will use the distributive property, which states that ${$ a(b + c) = ab + ac$}$. We will multiply each term in the first expression by each term in the second expression.

Step 1: Multiply the First Term in the First Expression by Each Term in the Second Expression

We will multiply the first term, ${ $3\$}$ , by each term in the second expression, ${ $3 - 8x\$}$ .

${ $3(3) = 9\$}$ ${ $3(-8x) = -24x\$}$

Step 2: Multiply the Second Term in the First Expression by Each Term in the Second Expression

We will multiply the second term, ${$ -4x$}$, by each term in the second expression, ${ $3 - 8x\$}$ .

${$ -4x(3) = -12x$}{ $-4x(-8x) = 32x^2\$}$

Step 3: Combine the Terms

Now that we have multiplied each term in the first expression by each term in the second expression, we will combine the terms.

${ $9 - 24x - 12x + 32x^2\$}$

Step 4: Simplify the Expression

We can simplify the expression by combining like terms.

${ $9 - 36x + 32x^2\$}$

Conclusion

Multiplying and simplifying algebraic expressions is a crucial skill that helps us solve equations and inequalities. In this article, we focused on multiplying and simplifying the expression ${$ (3 - 4x)(3 - 8x)$}$. We broke down the process into manageable steps, making it easier to understand and apply. By following these steps, you can multiply and simplify any algebraic expression.

Tips and Tricks

When multiplying expressions, use the distributive property to break down the process into manageable steps.
Combine like terms to simplify the expression.
Use parentheses to group terms and make it easier to multiply and simplify expressions.

Common Mistakes to Avoid

Failing to use the distributive property when multiplying expressions.
Not combining like terms to simplify the expression.
Not using parentheses to group terms and make it easier to multiply and simplify expressions.

Real-World Applications

Multiplying and simplifying algebraic expressions has many real-world applications. For example:

In physics, we use algebraic expressions to describe the motion of objects.
In engineering, we use algebraic expressions to design and optimize systems.
In economics, we use algebraic expressions to model and analyze economic systems.

Practice Problems

Try multiplying and simplifying the following expressions:

${$ (2x + 3)(x - 4)$}$
${$ (x + 2)(x + 5)$}$
${$ (3x - 2)(2x + 1)$}$

Conclusion

$Multiplying and simplifying algebraic expressions is a crucial skill that helps us solve equations and inequalities. In this article, we focused on multiplying and simplifying the expression ${$(3 - 4x)(3 - 8x)\$}$. We broke down the process into manageable steps, making it easier to understand and apply. By following these steps, you can multiply and simplify any algebraic expression.<br/> **Multiplying and Simplifying Algebraic Expressions: A Q&A Guide**$

Introduction

In our previous article, we discussed how to multiply and simplify algebraic expressions. In this article, we will answer some frequently asked questions about multiplying and simplifying algebraic expressions.

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. It states that ${$ a(b + c) = ab + ac$}$.

Q: How do I multiply two binomials?

A: To multiply two binomials, we use the distributive property to multiply each term in the first binomial by each term in the second binomial. We then combine the terms to simplify the expression.

Q: What is the difference between multiplying and simplifying?

A: Multiplying is the process of combining two or more expressions to form a new expression. Simplifying is the process of combining like terms to make the expression easier to read and understand.

Q: How do I know when to use the distributive property?

A: You should use the distributive property whenever you need to multiply a single term by two or more terms.

Q: Can I multiply expressions with variables and constants?

A: Yes, you can multiply expressions with variables and constants. When multiplying variables and constants, you multiply the coefficients (numbers) and the variables separately.

Q: How do I simplify an expression with multiple terms?

A: To simplify an expression with multiple terms, you combine like terms by adding or subtracting the coefficients of the variables.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Q: Can I use the distributive property to multiply expressions with exponents?

A: Yes, you can use the distributive property to multiply expressions with exponents. When multiplying expressions with exponents, you multiply the exponents separately.

Q: How do I multiply expressions with negative exponents?

A: To multiply expressions with negative exponents, you multiply the exponents separately and change the sign of the result.

Q: Can I simplify expressions with variables and constants?

A: Yes, you can simplify expressions with variables and constants. When simplifying expressions with variables and constants, you combine like terms by adding or subtracting the coefficients of the variables.

Q: How do I know when to use the distributive property to simplify an expression?

A: You should use the distributive property to simplify an expression when you have multiple terms with the same variable.

Q: Can I use the distributive property to multiply expressions with fractions?

A: Yes, you can use the distributive property to multiply expressions with fractions. When multiplying expressions with fractions, you multiply the numerators and denominators separately.

Conclusion

Multiplying and simplifying algebraic expressions is a crucial skill that helps us solve equations and inequalities. In this article, we answered some frequently asked questions about multiplying and simplifying algebraic expressions. By following the steps and rules outlined in this article, you can multiply and simplify any algebraic expression.

Practice Problems

Try multiplying and simplifying the following expressions:

${$ (2x + 3)(x - 4)$}$
${$ (x + 2)(x + 5)$}$
${$ (3x - 2)(2x + 1)$}$

Tips and Tricks

Use the distributive property to multiply expressions with variables and constants.
Combine like terms to simplify the expression.
Use parentheses to group terms and make it easier to multiply and simplify expressions.

Common Mistakes to Avoid

Failing to use the distributive property when multiplying expressions.
Not combining like terms to simplify the expression.
Not using parentheses to group terms and make it easier to multiply and simplify expressions.