Get the most out of your questions with IDNLearn.com's extensive resources. Whether it's a simple query or a complex problem, our experts have the answers you need.
Sagot :
To solve the given expression [tex]\(3(x - 7) + 4(x^2 - 2x + 9)\)[/tex] and determine which of the provided options it is equivalent to, let's break down the expression step by step.
1. Distribute the constants inside the parentheses:
- For [tex]\(3(x - 7)\)[/tex]:
[tex]\[ 3(x - 7) = 3x - 21 \][/tex]
- For [tex]\(4(x^2 - 2x + 9)\)[/tex]:
[tex]\[ 4(x^2 - 2x + 9) = 4x^2 - 8x + 36 \][/tex]
2. Combine the distributed parts:
[tex]\[ 3x - 21 + 4x^2 - 8x + 36 \][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ 4x^2 \][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ 3x - 8x = -5x \][/tex]
- Combine the constant terms:
[tex]\[ -21 + 36 = 15 \][/tex]
4. Write the simplified expression:
[tex]\[ 4x^2 - 5x + 15 \][/tex]
Therefore, the expression [tex]\(3(x-7) + 4(x^2 - 2x + 9)\)[/tex] simplifies to [tex]\(4x^2 - 5x + 15\)[/tex].
Thus, the correct answer is:
[tex]\[ 4x^2 - 5x + 15 \][/tex]
1. Distribute the constants inside the parentheses:
- For [tex]\(3(x - 7)\)[/tex]:
[tex]\[ 3(x - 7) = 3x - 21 \][/tex]
- For [tex]\(4(x^2 - 2x + 9)\)[/tex]:
[tex]\[ 4(x^2 - 2x + 9) = 4x^2 - 8x + 36 \][/tex]
2. Combine the distributed parts:
[tex]\[ 3x - 21 + 4x^2 - 8x + 36 \][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ 4x^2 \][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ 3x - 8x = -5x \][/tex]
- Combine the constant terms:
[tex]\[ -21 + 36 = 15 \][/tex]
4. Write the simplified expression:
[tex]\[ 4x^2 - 5x + 15 \][/tex]
Therefore, the expression [tex]\(3(x-7) + 4(x^2 - 2x + 9)\)[/tex] simplifies to [tex]\(4x^2 - 5x + 15\)[/tex].
Thus, the correct answer is:
[tex]\[ 4x^2 - 5x + 15 \][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.