Simplify: 4 - 12xy + 24xz​

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific algebraic expression: 4 - 12xy + 24xz. We will break down the expression into smaller parts, identify the like terms, and combine them to simplify the expression.

Understanding the Expression

Before we start simplifying the expression, let's take a closer look at it. The expression is: 4 - 12xy + 24xz. It consists of three terms: a constant term (4), a product of two variables (12xy), and a product of two variables (24xz).

Like Terms

Like terms are terms that have the same variable(s) raised to the same power. In this expression, we have two like terms: 12xy and 24xz. Both terms have two variables (x and y, and x and z, respectively) raised to the same power (1).

Simplifying the Expression

To simplify the expression, we need to combine the like terms. We can do this by adding or subtracting the coefficients of the like terms. In this case, we have:

12xy - 12xy + 24xz

The first two terms (12xy and -12xy) cancel each other out, leaving us with:

24xz

Step-by-Step Solution

Here's a step-by-step solution to simplify the expression:

  1. Identify the like terms: The like terms in the expression are 12xy and 24xz.
  2. Combine the like terms: We can combine the like terms by adding or subtracting their coefficients. In this case, we have: 12xy - 12xy + 24xz
  3. Simplify the expression: The first two terms (12xy and -12xy) cancel each other out, leaving us with: 24xz

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By identifying the like terms and combining them, we can simplify complex expressions and make them easier to work with. In this article, we simplified the expression 4 - 12xy + 24xz by combining the like terms and canceling out the first two terms.

Common Mistakes to Avoid

When simplifying algebraic expressions, there are several common mistakes to avoid:

  • Not identifying like terms: Make sure to identify the like terms in the expression before combining them.
  • Not combining like terms: Combine the like terms by adding or subtracting their coefficients.
  • Not canceling out terms: Cancel out the terms that cancel each other out.

Real-World Applications

Simplifying algebraic expressions has many real-world applications. For example:

  • Physics: Simplifying algebraic expressions is essential in physics, where complex equations are used to describe the behavior of physical systems.
  • Engineering: Simplifying algebraic expressions is also essential in engineering, where complex equations are used to design and optimize systems.
  • Computer Science: Simplifying algebraic expressions is also used in computer science, where complex algorithms are used to solve problems.

Practice Problems

Here are some practice problems to help you simplify algebraic expressions:

  • Simplify the expression: 3x^2 - 2x^2 + 5x
  • Simplify the expression: 2y^2 - 3y^2 + 4y
  • Simplify the expression: 4z^2 - 2z^2 + 3z

Conclusion

Introduction

In our previous article, we discussed how to simplify algebraic expressions by identifying like terms and combining them. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable(s) 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 identify like terms?

A: To identify like terms, look for terms that have the same variable(s) raised to the same power. You can also use the distributive property to rewrite the expression and make it easier to identify like terms.

Q: Can I combine like terms that have different coefficients?

A: Yes, you can combine like terms that have different coefficients. For example, 2x and 3x can be combined to get 5x.

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

A: The order of operations when simplifying algebraic expressions 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: Can I simplify an expression that has variables with different exponents?

A: Yes, you can simplify an expression that has variables with different exponents. For example, 2x^2 and 3x can be combined to get 2x^2 + 3x.

Q: How do I simplify an expression that has a negative coefficient?

A: To simplify an expression that has a negative coefficient, you can rewrite the expression with a positive coefficient and then add or subtract the terms. For example, -2x can be rewritten as -2x = -2x + 0x, and then simplified to -2x.

Q: Can I simplify an expression that has a fraction?

A: Yes, you can simplify an expression that has a fraction. To do this, you can multiply the numerator and denominator by the same value to eliminate the fraction. For example, 1/2x can be rewritten as (1/2)x = (1/2)x(2/2) = x/2.

Q: How do I simplify an expression that has a variable in the denominator?

A: To simplify an expression that has a variable in the denominator, you can multiply the numerator and denominator by the same value to eliminate the variable in the denominator. For example, 1/x can be rewritten as (1/x)(x/x) = 1/x^2.

Q: Can I simplify an expression that has a radical?

A: Yes, you can simplify an expression that has a radical. To do this, you can multiply the numerator and denominator by the same value to eliminate the radical. For example, √x can be rewritten as (√x)(√x) = x.

Q: How do I simplify an expression that has a complex number?

A: To simplify an expression that has a complex number, you can use the distributive property to rewrite the expression and then combine like terms. For example, 2 + 3i can be rewritten as 2 + 3i = 2 + 3i(1 + 1i) = 2 + 3i + 3i^2.

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By identifying like terms and combining them, we can simplify complex expressions and make them easier to work with. In this article, we answered some frequently asked questions about simplifying algebraic expressions and provided examples to illustrate the concepts.

Practice Problems

Here are some practice problems to help you simplify algebraic expressions:

  • Simplify the expression: 2x^2 - 3x^2 + 4x
  • Simplify the expression: 1/2x - 1/4x + 1/8x
  • Simplify the expression: √x + √y - √z

Real-World Applications

Simplifying algebraic expressions has many real-world applications. For example:

  • Physics: Simplifying algebraic expressions is essential in physics, where complex equations are used to describe the behavior of physical systems.
  • Engineering: Simplifying algebraic expressions is also essential in engineering, where complex equations are used to design and optimize systems.
  • Computer Science: Simplifying algebraic expressions is also used in computer science, where complex algorithms are used to solve problems.

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By identifying like terms and combining them, we can simplify complex expressions and make them easier to work with. In this article, we answered some frequently asked questions about simplifying algebraic expressions and provided examples to illustrate the concepts.