Select The Correct Answer.What Is The Simplified Form Of This Expression?$(-3x^2 + 4x) + (2x^2 - X - 11$\]A. $-x^2 + 5x - 11$ B. $-x^2 + 3x - 11$ C. $-x^2 + 3x + 11$ D. $-x^2 + 5x + 11$

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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 explore the process of simplifying algebraic expressions, using the given expression as an example. We will break down the expression into smaller parts, combine like terms, and arrive at the simplified form.

The Given Expression

The given expression is:

(−3x2+4x)+(2x2−x−11)(-3x^2 + 4x) + (2x^2 - x - 11)

Step 1: Distributive Property

To simplify the expression, we need to apply the distributive property, which states that for any real numbers a, b, and c:

a(b + c) = ab + ac

Using this property, we can rewrite the expression as:

(−3x2+4x)+(2x2−x−11)(-3x^2 + 4x) + (2x^2 - x - 11)

=(−3x2)+(4x)+(2x2)+(−x)+(−11)= (-3x^2) + (4x) + (2x^2) + (-x) + (-11)

Step 2: Combine Like Terms

Now that we have applied the distributive property, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable x^2, and two terms with the variable x.

Combining the like terms, we get:

=(−3x2+2x2)+(4x−x)+(−11)= (-3x^2 + 2x^2) + (4x - x) + (-11)

=−x2+3x−11= -x^2 + 3x - 11

Conclusion

The simplified form of the expression is:

−x2+3x−11-x^2 + 3x - 11

This is the correct answer.

Comparison with Options

Let's compare our answer with the options provided:

A. −x2+5x−11-x^2 + 5x - 11 B. −x2+3x−11-x^2 + 3x - 11 C. −x2+3x+11-x^2 + 3x + 11 D. −x2+5x+11-x^2 + 5x + 11

Our answer matches option B.

Tips and Tricks

When simplifying algebraic expressions, remember to:

  • Apply the distributive property to rewrite the expression
  • Combine like terms to simplify the expression
  • Check your answer by comparing it with the options provided

By following these steps and tips, you can simplify algebraic expressions with ease.

Common Mistakes to Avoid

When simplifying algebraic expressions, be careful not to:

  • Forget to apply the distributive property
  • Combine unlike terms
  • Neglect to check your answer

By avoiding these common mistakes, you can ensure that your answer is accurate and complete.

Real-World Applications

Simplifying algebraic expressions has many real-world applications, such as:

  • Solving systems of equations
  • Finding the area and perimeter of shapes
  • Modeling population growth and decay

By mastering the skill of simplifying algebraic expressions, you can apply it to a wide range of problems and situations.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill to master in mathematics. By applying the distributive property, combining like terms, and checking your answer, you can arrive at the simplified form of an expression. Remember to avoid common mistakes and apply this skill to real-world problems. With practice and patience, you can become proficient in simplifying algebraic expressions.