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]
