11) X³-2x² 4 + 3xy² -64​

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Introduction

In this article, we will be discussing the given mathematical expression: x³-2x² + 4 + 3xy² -64. We will break down the expression, identify its components, and then simplify it to its most basic form. This will involve using various mathematical operations and techniques, including addition, subtraction, multiplication, and exponentiation.

Breaking Down the Expression

The given expression is a polynomial expression, which means it is a sum of terms, each of which is a product of variables and coefficients. The expression can be broken down into its individual components as follows:

  • x³: This is a term with a variable x raised to the power of 3.
  • -2x²: This is a term with a variable x raised to the power of 2, multiplied by -2.
  • +4: This is a constant term, which means it is a number that does not have any variables.
  • +3xy²: This is a term with two variables, x and y, raised to the power of 1 and 2 respectively, multiplied by 3.
  • -64: This is another constant term.

Simplifying the Expression

To simplify the expression, we need to combine like terms. Like terms are terms that have the same variable(s) raised to the same power. In this case, we can combine the terms x³ and -2x², as well as the constant terms 4 and -64.

Combining Like Terms

We can start by combining the terms x³ and -2x². To do this, we need to subtract 2x² from x³. This gives us:

x³ - 2x² = x³ - x² - x²

We can then combine the two -x² terms to get:

x³ - 2x² = x³ - 2x²

Next, we can combine the constant terms 4 and -64. To do this, we need to subtract 64 from 4. This gives us:

4 - 64 = -60

So, the simplified expression is:

x³ - 2x² + 3xy² - 60

Factoring Out Common Terms

We can also factor out common terms from the expression. In this case, we can factor out a -1 from the terms -2x² and -60. This gives us:

x³ - 2x² + 3xy² - 60 = -1(2x² + 60) + x³ + 3xy²

We can then factor out a 2 from the terms 2x² and 60. This gives us:

x³ - 2x² + 3xy² - 60 = -1(2(x² + 30)) + x³ + 3xy²

Final Simplification

We can now simplify the expression further by combining the terms x³ and 3xy². To do this, we need to add 3xy² to x³. This gives us:

x³ + 3xy² = x³ + 3xy²

So, the final simplified expression is:

x³ - 2x² + 3xy² - 60 = -1(2(x² + 30)) + x³ + 3xy²

Conclusion

In this article, we have broken down the given mathematical expression, identified its components, and then simplified it to its most basic form. We have used various mathematical operations and techniques, including addition, subtraction, multiplication, and exponentiation. The final simplified expression is x³ - 2x² + 3xy² - 60 = -1(2(x² + 30)) + x³ + 3xy².

Frequently Asked Questions

  • What is the given mathematical expression? The given mathematical expression is x³-2x² + 4 + 3xy² -64.
  • How do we simplify the expression? We simplify the expression by combining like terms and factoring out common terms.
  • What is the final simplified expression? The final simplified expression is x³ - 2x² + 3xy² - 60 = -1(2(x² + 30)) + x³ + 3xy².

Key Takeaways

  • The given mathematical expression is x³-2x² + 4 + 3xy² -64.
  • We simplify the expression by combining like terms and factoring out common terms.
  • The final simplified expression is x³ - 2x² + 3xy² - 60 = -1(2(x² + 30)) + x³ + 3xy².

Further Reading

If you want to learn more about simplifying mathematical expressions, I recommend checking out the following resources:

  • Khan Academy: Simplifying Expressions
  • Mathway: Simplifying Expressions
  • Wolfram Alpha: Simplifying Expressions

References

Introduction

In our previous article, we discussed the given mathematical expression: x³-2x² + 4 + 3xy² -64. We broke down the expression, identified its components, and then simplified it to its most basic form. In this article, we will answer some frequently asked questions related to simplifying mathematical expressions.

Q&A

Q1: What is the first step in simplifying a mathematical expression?

A1: The first step in simplifying a mathematical expression is to identify the like terms. Like terms are terms that have the same variable(s) raised to the same power.

Q2: How do we combine like terms?

A2: To combine like terms, we need to add or subtract the coefficients of the like terms. For example, if we have two terms with the same variable raised to the same power, we can combine them by adding or subtracting their coefficients.

Q3: What is the difference between combining like terms and factoring out common terms?

A3: Combining like terms involves adding or subtracting the coefficients of like terms, while factoring out common terms involves expressing a term as a product of a common factor and a remaining term.

Q4: How do we factor out common terms?

A4: To factor out common terms, we need to identify the common factor and express the term as a product of the common factor and a remaining term. For example, if we have a term with a common factor of 2, we can factor it out as 2 times the remaining term.

Q5: What is the final simplified expression for the given mathematical expression?

A5: The final simplified expression for the given mathematical expression is x³ - 2x² + 3xy² - 60 = -1(2(x² + 30)) + x³ + 3xy².

Q6: How do we check if the simplified expression is correct?

A6: To check if the simplified expression is correct, we need to substitute the original expression into the simplified expression and verify that they are equivalent.

Q7: What are some common mistakes to avoid when simplifying mathematical expressions?

A7: Some common mistakes to avoid when simplifying mathematical expressions include:

  • Not identifying like terms
  • Not combining like terms correctly
  • Not factoring out common terms correctly
  • Not checking the simplified expression for correctness

Conclusion

In this article, we have answered some frequently asked questions related to simplifying mathematical expressions. We have discussed the first step in simplifying a mathematical expression, combining like terms, factoring out common terms, and checking the simplified expression for correctness. We have also identified some common mistakes to avoid when simplifying mathematical expressions.

Frequently Asked Questions

  • What is the first step in simplifying a mathematical expression? The first step in simplifying a mathematical expression is to identify the like terms.
  • How do we combine like terms? We combine like terms by adding or subtracting the coefficients of the like terms.
  • What is the difference between combining like terms and factoring out common terms? Combining like terms involves adding or subtracting the coefficients of like terms, while factoring out common terms involves expressing a term as a product of a common factor and a remaining term.
  • How do we factor out common terms? We factor out common terms by identifying the common factor and expressing the term as a product of the common factor and a remaining term.

Key Takeaways

  • The first step in simplifying a mathematical expression is to identify the like terms.
  • We combine like terms by adding or subtracting the coefficients of the like terms.
  • Factoring out common terms involves expressing a term as a product of a common factor and a remaining term.
  • We check the simplified expression for correctness by substituting the original expression into the simplified expression.

Further Reading

If you want to learn more about simplifying mathematical expressions, I recommend checking out the following resources:

  • Khan Academy: Simplifying Expressions
  • Mathway: Simplifying Expressions
  • Wolfram Alpha: Simplifying Expressions

References