Golution 9) (8x+5x+(6x³-3x²)

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on simplifying a specific type of algebraic expression, known as a polynomial expression. We will use the expression 8x + 5x + (6x³ - 3x²) as an example and walk through the step-by-step process of simplifying it.

What is a Polynomial Expression?

A polynomial expression is an expression that consists of variables and coefficients combined using only addition, subtraction, and multiplication. It can be written in the form:

a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0

where a_n, a_(n-1), ..., a_1, and a_0 are coefficients, and x is the variable.

Simplifying the Expression

Now, let's simplify the expression 8x + 5x + (6x³ - 3x²). To do this, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses first.
  2. Exponents: Evaluate any exponents 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.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is 6x³ - 3x². We can leave this expression as is for now.

Step 2: Combine Like Terms

Now, let's combine like terms in the expression 8x + 5x + (6x³ - 3x²). Like terms are terms that have the same variable and exponent. In this case, we have two like terms: 8x and 5x.

To combine these terms, we add their coefficients:

8x + 5x = (8 + 5)x = 13x

So, the expression becomes 13x + (6x³ - 3x²).

Step 3: Simplify the Expression

Now, let's simplify the expression 13x + (6x³ - 3x²). We can rewrite this expression as:

13x + 6x³ - 3x²

This is the simplified expression.

Conclusion

Simplifying algebraic expressions is an important skill to master in mathematics. By following the order of operations and combining like terms, we can simplify complex expressions and make them easier to work with. In this article, we used the expression 8x + 5x + (6x³ - 3x²) as an example and walked through the step-by-step process of simplifying it.

Tips and Tricks

Here are some tips and tricks to help you simplify algebraic expressions:

  • Use the distributive property: The distributive property states that a(b + c) = ab + ac. This can help you simplify expressions by distributing the terms inside the parentheses.
  • Combine like terms: Like terms are terms that have the same variable and exponent. Combining like terms can help you simplify expressions by adding or subtracting their coefficients.
  • Use the order of operations: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an expression.

Practice Problems

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

  • Simplify the expression 2x + 3x + (4x³ - 2x²)
  • Simplify the expression 5x - 2x + (3x² - x)
  • Simplify the expression 8x + 2x + (6x³ - 4x²)

Real-World Applications

Simplifying algebraic expressions has many real-world applications. Here are a few examples:

  • Science and Engineering: Algebraic expressions are used to model real-world phenomena, such as the motion of objects or the behavior of electrical circuits.
  • Economics: Algebraic expressions are used to model economic systems, such as supply and demand curves.
  • Computer Science: Algebraic expressions are used to model algorithms and data structures.

Conclusion

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an expression. The order of operations is:

  1. Parentheses: Evaluate the expression inside the parentheses first.
  2. Exponents: Evaluate any exponents 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: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x and 3x are like terms because they both have the variable x and the exponent 1.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract their coefficients. For example, to combine 2x and 3x, you add their coefficients:

2x + 3x = (2 + 3)x = 5x

Q: What is the distributive property?

A: The distributive property is a rule that states that a(b + c) = ab + ac. This can help you simplify expressions by distributing the terms inside the parentheses.

Q: How do I use the distributive property?

A: To use the distributive property, you multiply the term outside the parentheses by each term inside the parentheses. For example, to simplify 2(x + 3), you multiply 2 by each term inside the parentheses:

2(x + 3) = 2x + 6

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

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

  • Not following the order of operations: Make sure to evaluate the expression inside the parentheses first, then evaluate any exponents, and so on.
  • Not combining like terms: Make sure to combine like terms by adding or subtracting their coefficients.
  • Not using the distributive property: Make sure to use the distributive property to simplify expressions with parentheses.

Q: How do I check my work when simplifying algebraic expressions?

A: To check your work when simplifying algebraic expressions, you can:

  • Plug in values: Plug in values for the variable to see if the expression simplifies correctly.
  • Use a calculator: Use a calculator to simplify the expression and see if it matches your answer.
  • Check your work step-by-step: Check your work step-by-step to make sure you followed the order of operations and combined like terms correctly.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

  • Science and Engineering: Algebraic expressions are used to model real-world phenomena, such as the motion of objects or the behavior of electrical circuits.
  • Economics: Algebraic expressions are used to model economic systems, such as supply and demand curves.
  • Computer Science: Algebraic expressions are used to model algorithms and data structures.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by:

  • Solving practice problems: Solve practice problems to help you practice simplifying algebraic expressions.
  • Using online resources: Use online resources, such as video tutorials or practice problems, to help you practice simplifying algebraic expressions.
  • Working with a tutor: Work with a tutor to help you practice simplifying algebraic expressions and get feedback on your work.