Get comprehensive solutions to your problems with IDNLearn.com. Join our knowledgeable community and get detailed, reliable answers to all your questions.

Select the correct answer.

Which expression is equivalent to the given expression?
[tex]\[ 3(x-7) + 4\left(x^2 - 2x + 9\right) \][/tex]

A. [tex]\(4x^2 - 5x + 15\)[/tex]

B. [tex]\(4x^2 + x - 12\)[/tex]

C. [tex]\(4x^2 + 11x - 15\)[/tex]

D. [tex]\(4x^2 + 5x - 16\)[/tex]


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]