Simplify The Expression: $\left(7 X^2\right)(-3 X)\left(2 X^2\right)(3)=$

Feb 26, 2025 by ADMIN 74 views

$Simplify the Expression: $\left(7 x^2\right)(-3 x)\left(2 x^2\right)(3)$$

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and manipulate mathematical statements. When we simplify an expression, we combine like terms and eliminate any unnecessary components. In this article, we will focus on simplifying the given expression $\left(7 x^2\right)(-3 x)\left(2 x^2\right)(3)$ using the rules of exponents and basic algebra.

Understanding the Expression

The given expression is a product of four terms: $\left(7 x^2\right)$ , $(-3 x)$ , $\left(2 x^2\right)$ , and $(3)$ . To simplify this expression, we need to apply the rules of exponents and combine like terms.

Applying the Rules of Exponents

When we multiply two or more terms with the same base, we add their exponents. In this case, we have two terms with the base $x$ , namely $\left(7 x^2\right)$ and $(-3 x)$ . We can combine these two terms by adding their exponents:

\left(7 x^2\right)(-3 x) = 7 x^{2+1}(-3) = -21 x^3

Similarly, we can combine the other two terms, $\left(2 x^2\right)$ and $(3)$ , by adding their exponents:

\left(2 x^2\right)(3) = 6 x^2

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression by multiplying the remaining terms:

\left(7 x^2\right)(-3 x)\left(2 x^2\right)(3) = (-21 x^3)(6 x^2)

Using the rule of exponents, we can add the exponents of the two terms:

(-21 x^3)(6 x^2) = -126 x^{3+2} = -126 x^5

Conclusion

In this article, we simplified the expression $\left(7 x^2\right)(-3 x)\left(2 x^2\right)(3)$ using the rules of exponents and basic algebra. We combined like terms and eliminated any unnecessary components to arrive at the final simplified expression: $-126 x^5$ . This example demonstrates the importance of simplifying expressions in algebra and how it can help us solve equations and manipulate mathematical statements.

Tips and Tricks

When simplifying expressions, always look for like terms and combine them using the rules of exponents.
Use the rule of exponents to add the exponents of two or more terms with the same base.
Eliminate any unnecessary components, such as parentheses or brackets, to simplify the expression.

Common Mistakes

Failing to combine like terms can lead to incorrect simplifications.
Not using the rule of exponents can result in incorrect exponents.
Not eliminating unnecessary components can make the expression more complicated than it needs to be.

Real-World Applications

Simplifying expressions is a crucial skill in many real-world applications, including:

Physics: Simplifying expressions is essential in physics to solve equations and manipulate mathematical statements.
Engineering: Engineers use simplifying expressions to design and optimize systems.
Computer Science: Simplifying expressions is used in computer science to optimize algorithms and data structures.

Final Thoughts

Simplifying expressions is a fundamental skill in algebra that helps us solve equations and manipulate mathematical statements. By combining like terms and applying the rules of exponents, we can simplify complex expressions and arrive at the final answer. In this article, we simplified the expression $\left(7 x^2\right)(-3 x)\left(2 x^2\right)(3)$ using the rules of exponents and basic algebra. We hope this example has demonstrated the importance of simplifying expressions in algebra and how it can help us solve equations and manipulate mathematical statements.

Introduction

In our previous article, we simplified the expression $\left(7 x^2\right)(-3 x)\left(2 x^2\right)(3)$ using the rules of exponents and basic algebra. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q&A

Q: What is the first step in simplifying an expression?

A: The first step in simplifying an expression is to look for like terms and combine them using the rules of exponents.

Q: How do I combine like terms?

A: To combine like terms, you need to add their coefficients and keep the same variable and exponent.

Q: What is the rule of exponents?

A: The rule of exponents states that when you multiply two or more terms with the same base, you add their exponents.

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to follow the order of operations (PEMDAS):

Evaluate expressions inside parentheses
Evaluate any exponential expressions
Evaluate any multiplication and division expressions
Evaluate any addition and subtraction expressions

Q: Can I simplify an expression with variables?

A: Yes, you can simplify an expression with variables by combining like terms and applying the rules of exponents.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to multiply the numerator and denominator by the same value to eliminate the fraction.

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

A: Simplifying an expression involves combining like terms and applying the rules of exponents to arrive at a simpler expression. Solving an equation involves finding the value of the variable that makes the equation true.

Q: Can I simplify an expression with negative numbers?

A: Yes, you can simplify an expression with negative numbers by combining like terms and applying the rules of exponents.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you need to apply the rule of exponents, which states that when you multiply two or more terms with the same base, you add their exponents.

Q: Can I simplify an expression with radicals?

A: Yes, you can simplify an expression with radicals by combining like terms and applying the rules of exponents.