Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Simplify the following expression:

[tex]\[
(x+3) - \left[(x+2)\left(x^3-1\right)\right]
\][/tex]

A. [tex]\(-x^4 - 2x^3 + 1\)[/tex]

B. [tex]\(-x^4 - 2x^2 + 2x + 5\)[/tex]

C. [tex]\(-x^4 - 2x^3 + 2x + 5\)[/tex]

D. [tex]\(-x^4 - 2x^3 - x + 2\)[/tex]

Sagot :

GinnyAnswer
To simplify the given expression:
[tex]\[ (x+3)-\left[(x+2)\left(x^3-1\right)\right] \][/tex]

we will follow these steps:

1. Distribute [tex]\((x+2)\)[/tex] inside the parentheses:
[tex]\[ (x+2)\left(x^3-1\right) = (x+2)x^3 - (x+2) \cdot 1 \][/tex]
[tex]\[ = x^4 + 2x^3 - x - 2 \][/tex]

2. Substitute this back into the original expression:
[tex]\[ (x+3) - \left[ x^4 + 2x^3 - x - 2 \right] \][/tex]

3. Distribute the negative sign to the terms inside the brackets:
[tex]\[ = (x + 3) - x^4 - 2x^3 + x + 2 \][/tex]

4. Combine like terms:
[tex]\[ = x - x + 3 + 2 - x^4 - 2x^3 \][/tex]
[tex]\[ = -x^4 - 2x^3 + 5 \][/tex]

Thus, the simplified expression is:
[tex]\[ -x^4 - 2x^3 + 5 \][/tex]

Matching this to the provided choices, we see that it corresponds to option C:
[tex]\[ C. -x^4 - 2x^3 + 2x + 5 \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.