Select the correct answer.

What is the simplified form of this expression?
[tex]\[ \left(5x^2 + 2x + 11\right) - \left(7 + 4x - 2x^2\right) \][/tex]

A. [tex]\(9 - 2x - 2x^2\)[/tex]
B. [tex]\(3x^2 + 6x + 4\)[/tex]
C. [tex]\(3x^2 - 2x + 4\)[/tex]
D. [tex]\(7x^2 - 2x + 4\)[/tex]



Answer :

To simplify the expression [tex]\((5x^2 + 2x + 11) - (7 + 4x - 2x^2)\)[/tex], follow these steps:

1. Distribute the minus sign across the second parenthesis:
This changes the sign of each term inside the second parenthesis.
[tex]\[ 5x^2 + 2x + 11 - 7 - 4x + 2x^2 \][/tex]

2. Combine like terms:
Group the terms with [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant terms together.
- For [tex]\(x^2\)[/tex] terms:
[tex]\[ 5x^2 + 2x^2 = 7x^2 \][/tex]
- For [tex]\(x\)[/tex] terms:
[tex]\[ 2x - 4x = -2x \][/tex]
- For the constant terms:
[tex]\[ 11 - 7 = 4 \][/tex]

3. Write the simplified expression:
Combining all the like terms, we get:
[tex]\[ 7x^2 - 2x + 4 \][/tex]

Therefore, the simplified form of the expression is:
[tex]\[ 7x^2 - 2x + 4 \][/tex]

The correct answer is:

D. [tex]\(7x^2 - 2x + 4\)[/tex]