Simplify The Following Expression: { -6x^2 + 2 + 7x^2 - 10x$}$

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will focus on simplifying a given algebraic expression, which involves combining like terms and rearranging the expression to its simplest form.

The Given Expression

The given expression is:

−6x2+2+7x2−10x-6x^2 + 2 + 7x^2 - 10x

Step 1: Identify Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, we can identify the following like terms:

  • −6x2-6x^2 and 7x27x^2 are like terms because they both have the variable xx raised to the power of 2.
  • −10x-10x is a like term with itself, but it does not have a corresponding term to combine with.

Step 2: Combine Like Terms

Now that we have identified the like terms, we can combine them by adding or subtracting their coefficients. In this case, we can combine the like terms −6x2-6x^2 and 7x27x^2 by adding their coefficients:

−6x2+7x2=(7−6)x2=x2-6x^2 + 7x^2 = (7 - 6)x^2 = x^2

So, the expression now becomes:

x2+2−10xx^2 + 2 - 10x

Step 3: Rearrange the Expression

Now that we have combined the like terms, we can rearrange the expression to put it in a more simplified form. We can start by rearranging the terms in descending order of their exponents:

x2−10x+2x^2 - 10x + 2

The Final Simplified Expression

And there you have it! The final simplified expression is:

x2−10x+2x^2 - 10x + 2

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By identifying like terms and combining them, we can simplify complex expressions and make them easier to work with. In this article, we have walked through the step-by-step process of simplifying a given algebraic expression, and we have arrived at the final simplified expression.

Tips and Tricks

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

  • Identify like terms: Like terms are the key to simplifying algebraic expressions. Make sure to identify all the like terms in the expression.
  • Combine like terms: Once you have identified the like terms, combine them by adding or subtracting their coefficients.
  • Rearrange the expression: Finally, rearrange the expression to put it in a more simplified form.
  • Use the order of operations: When simplifying algebraic expressions, make sure to follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying algebraic expressions:

  • Not identifying like terms: Failing to identify like terms can lead to incorrect simplifications.
  • Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
  • Not rearranging the expression: Failing to rearrange the expression can lead to incorrect simplifications.

Real-World Applications

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 and the behavior of electrical circuits.
  • Economics: Algebraic expressions are used to model economic systems and make predictions about future economic trends.
  • Computer science: Algebraic expressions are used to write algorithms and solve problems in computer science.

Conclusion

Introduction

In our previous article, we walked through the step-by-step process of simplifying a given algebraic expression. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 2x2x and 5x5x are like terms because they both have the variable xx 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 raised to the same power. For example, in the expression 3x2+2x2+4x3x^2 + 2x^2 + 4x, the like terms are 3x23x^2 and 2x22x^2 because they both have the variable xx raised to the power of 2.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients. For example, in the expression 3x2+2x2+4x3x^2 + 2x^2 + 4x, the like terms 3x23x^2 and 2x22x^2 can be combined by adding their coefficients:

3x2+2x2=(3+2)x2=5x23x^2 + 2x^2 = (3 + 2)x^2 = 5x^2

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 simplifying algebraic expressions. The order of operations is:

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

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, follow these steps:

  1. Find the least common denominator (LCD): The LCD is the smallest number that both fractions can divide into evenly.
  2. Rewrite the fractions with the LCD: Rewrite each fraction with the LCD as the denominator.
  3. Combine the fractions: Add or subtract the numerators of the fractions.
  4. Simplify the resulting fraction: Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Q: How do I simplify an expression with negative exponents?

A: To simplify an expression with negative exponents, follow these steps:

  1. Rewrite the negative exponent as a positive exponent: Rewrite the negative exponent as a positive exponent by moving it to the other side of the fraction.
  2. Simplify the resulting fraction: Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

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

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

  • Not identifying like terms: Failing to identify like terms can lead to incorrect simplifications.
  • Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
  • Not rearranging the expression: Failing to rearrange the expression can lead to incorrect simplifications.
  • Not following the order of operations: Failing to follow the order of operations can lead to incorrect simplifications.

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By identifying like terms and combining them, we can simplify complex expressions and make them easier to work with. In this article, we have answered some frequently asked questions about simplifying algebraic expressions and provided tips and tricks to help you simplify expressions like a pro.