Which Expression Equals The Product Of $(x-3)(2x+1)$?A. $2x^2-7x-3$B. $ 2 X 2 − 5 X − 3 2x^2-5x-3 2 X 2 − 5 X − 3 [/tex]C. $3x-2$D. $6x^2$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific type of algebraic expression, namely the product of two binomials. We will use the given expression $(x-3)(2x+1)$ as an example and explore the different methods to solve it.

Understanding the Expression

The given expression is a product of two binomials, $(x-3)$ and $(2x+1)$. To solve this expression, we need to multiply the two binomials using the distributive property. The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$.

Multiplying Binomials

To multiply the two binomials, we will use the distributive property. We will multiply each term in the first binomial by each term in the second binomial.

$(x-3)(2x+1) = x(2x+1) - 3(2x+1)$

Now, we will multiply each term:

$x(2x+1) = 2x^2 + x$

$-3(2x+1) = -6x - 3$

Combining Like Terms

Now that we have multiplied each term, we can combine like terms. Like terms are terms that have the same variable raised to the same power.

$2x^2 + x - 6x - 3$

We can combine the like terms $x$ and $-6x$ to get:

$2x^2 - 5x - 3$

Evaluating the Answer Choices

Now that we have solved the expression, we can evaluate the answer choices. The answer choices are:

A. $2x^2-7x-3$ B. $2x^2-5x-3$ C. $3x-2$ D. $6x^2$

We can see that answer choice B matches our solution.

Conclusion

In this article, we solved the algebraic expression $(x-3)(2x+1)$ using the distributive property and combining like terms. We then evaluated the answer choices and found that answer choice B matches our solution. This exercise demonstrates the importance of understanding algebraic expressions and solving them using the correct methods.

Tips and Tricks

• When multiplying binomials, use the distributive property to multiply each term in the first binomial by each term in the second binomial.
• When combining like terms, look for terms that have the same variable raised to the same power.
• When evaluating answer choices, make sure to check each term carefully to ensure that it matches the solution.

Common Mistakes

• Failing to use the distributive property when multiplying binomials.
• Failing to combine like terms.
• Not checking each term carefully when evaluating answer choices.

Real-World Applications

Algebraic expressions are used in a wide range of real-world applications, including:

• Physics: Algebraic expressions are used to describe the motion of objects and the forces acting on them.
• Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and buildings.
• Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Final Thoughts

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Algebraic expressions are used to describe relationships between variables and constants.

Q: What is the distributive property?

A: The distributive property is a mathematical property that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This property is used to multiply binomials.

Q: How do I multiply binomials?

A: To multiply binomials, use the distributive property to multiply each term in the first binomial by each term in the second binomial. Then, combine like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $-3x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, $2x + 3x = 5x$.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, substitute the given values for the variables and perform the mathematical operations.

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 evaluating an algebraic expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, combine like terms and eliminate any unnecessary parentheses or brackets.

Q: What is the difference between an equation and an expression?

A: An equation is a statement that says two expressions are equal. An expression is a mathematical statement that contains variables and constants.

Q: How do I solve an equation?

A: To solve an equation, isolate the variable by performing inverse operations to both sides of the equation.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1. A quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I graph an algebraic expression?

A: To graph an algebraic expression, use a graphing calculator or graph paper to plot the points that satisfy the equation.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

• Linear expressions: $ax + b$
• Quadratic expressions: $ax^2 + bx + c$
• Polynomial expressions: $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$

Q: How do I use algebraic expressions in real-world applications?

A: Algebraic expressions are used in a wide range of real-world applications, including:

• Physics: Algebraic expressions are used to describe the motion of objects and the forces acting on them.
• Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and buildings.
• Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Conclusion

Algebraic expressions are a fundamental concept in mathematics, and understanding them is crucial for solving a wide range of problems. By mastering the concepts of algebraic expressions, you can apply them to real-world applications and make informed decisions.