Which Of The Following Simplifies To The Same Expression As $4x^2 - 3x^2 + 5x - 24$?A. $2(x-12)$ B. $ ( X + 6 ) ( X − 4 ) (x+6)(x-4) ( X + 6 ) ( X − 4 ) [/tex] C. $4x(x-6)$ D. $(x+8)(x-3)$

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill for students to master. In this article, we will explore the process of simplifying algebraic expressions, with a focus on the given expression $4x^2 - 3x^2 + 5x - 24$. We will examine each option and determine which one simplifies to the same expression.

Understanding the Given Expression

The given expression is $4x^2 - 3x^2 + 5x - 24$. To simplify this expression, we need to combine like terms. Like terms are terms that have the same variable raised to the same power.

4x^2 - 3x^2 + 5x - 24

We can start by combining the like terms:

(4x^2 - 3x^2) + 5x - 24

Next, we can simplify the expression by combining the like terms:

x^2 + 5x - 24

Option A: 2(x-12)

Let's examine option A: $2(x-12)$. To simplify this expression, we need to distribute the 2 to the terms inside the parentheses.

2(x-12)

Distributing the 2, we get:

2x - 24

This expression is not equivalent to the given expression $x^2 + 5x - 24$. Therefore, option A is not the correct answer.

Option B: (x+6)(x-4)

Let's examine option B: $(x+6)(x-4)$. To simplify this expression, we need to multiply the two binomials.

(x+6)(x-4)

Using the FOIL method (First, Outer, Inner, Last), we get:

x^2 - 4x + 6x - 24

Combining like terms, we get:

x^2 + 2x - 24

This expression is not equivalent to the given expression $x^2 + 5x - 24$. Therefore, option B is not the correct answer.

Option C: 4x(x-6)

Let's examine option C: $4x(x-6)$. To simplify this expression, we need to distribute the 4x to the terms inside the parentheses.

4x(x-6)

Distributing the 4x, we get:

4x^2 - 24x

This expression is not equivalent to the given expression $x^2 + 5x - 24$. Therefore, option C is not the correct answer.

Option D: (x+8)(x-3)

Let's examine option D: $(x+8)(x-3)$. To simplify this expression, we need to multiply the two binomials.

(x+8)(x-3)

Using the FOIL method (First, Outer, Inner, Last), we get:

x^2 - 3x + 8x - 24

Combining like terms, we get:

x^2 + 5x - 24

This expression is equivalent to the given expression $x^2 + 5x - 24$. Therefore, option D is the correct answer.

Conclusion

In conclusion, the correct answer is option D: $(x+8)(x-3)$. This expression simplifies to the same expression as $4x^2 - 3x^2 + 5x - 24$. We hope this article has provided a clear understanding of how to simplify algebraic expressions and has helped students master this important skill.

Final Answer

The final answer is: D\boxed{D}