Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Choose the correct simplification of [tex]\((6x - 5)(2x^2 - 3x - 6)\)[/tex].

A. [tex]\(12x^3 + 28x^2 + 21x + 30\)[/tex]
B. [tex]\(12x^3 - 28x^2 - 21x + 30\)[/tex]
C. [tex]\(12x^3 + 28x^2 - 21x + 30\)[/tex]
D. [tex]\(12x^3 - 28x^2 - 21x - 30\)[/tex]

Sagot :

GinnyAnswer
To simplify the expression [tex]\((6x - 5)(2x^2 - 3x - 6)\)[/tex], let's break it down step by step using the distributive property (also known as the FOIL method for binomials):

1. Distribute [tex]\(6x\)[/tex]:
[tex]\[ 6x \cdot (2x^2 - 3x - 6) = 6x \cdot 2x^2 + 6x \cdot (-3x) + 6x \cdot (-6) \][/tex]

2. Calculate each term individually:
- [tex]\(6x \cdot 2x^2 = 12x^3\)[/tex]
- [tex]\(6x \cdot (-3x) = -18x^2\)[/tex]
- [tex]\(6x \cdot (-6) = -36x\)[/tex]

3. Combine the results from distribution of [tex]\(6x\)[/tex]:
[tex]\[ 12x^3 - 18x^2 - 36x \][/tex]

4. Distribute [tex]\(-5\)[/tex]:
[tex]\[ -5 \cdot (2x^2 - 3x - 6) = -5 \cdot 2x^2 + (-5) \cdot (-3x) + (-5) \cdot (-6) \][/tex]

5. Calculate each term individually:
- [tex]\(-5 \cdot 2x^2 = -10x^2\)[/tex]
- [tex]\(-5 \cdot (-3x) = 15x\)[/tex]
- [tex]\(-5 \cdot (-6) = 30\)[/tex]

6. Combine the results from distribution of [tex]\(-5\)[/tex]:
[tex]\[ -10x^2 + 15x + 30 \][/tex]

7. Add all the terms from both distributions together:
[tex]\[ (12x^3 - 18x^2 - 36x) + (-10x^2 + 15x + 30) \][/tex]

8. Combine like terms:
[tex]\[ 12x^3 + (-18x^2 - 10x^2) + (-36x + 15x) + 30 \][/tex]
Simplifying each group of like terms:
- [tex]\(12x^3\)[/tex]
- [tex]\(-18x^2 - 10x^2 = -28x^2\)[/tex]
- [tex]\(-36x + 15x = -21x\)[/tex]
- [tex]\(30\)[/tex]

9. Combine all the simplified terms:
[tex]\[ 12x^3 - 28x^2 - 21x + 30 \][/tex]

So, the correct simplification of [tex]\((6x - 5)(2x^2 - 3x - 6)\)[/tex] is:

[tex]\[ \boxed{12x^3 - 28x^2 - 21x + 30} \][/tex]

The correct answer from the given choices is:

[tex]\(\boxed{12 x^3 - 28 x^2 - 21 x + 30}\)[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.