Which of the following correctly simplifies (9x^2 +17x +13) -(2x^2 +12x +11)?

Answer 1

To simplify the expression \((9x^2 + 17x + 13) - (2x^2 + 12x + 11)\), we first distribute the negative sign across the second polynomial:

\[ 9x^2 + 17x + 13 - 2x^2 - 12x - 11 \]

Next, we combine like terms. We will group the \(x^2\) terms, the \(x\) terms, and the constant terms together:

1. Combine the \(x^2\) terms: \[ 9x^2 - 2x^2 = 7x^2 \]

2. Combine the \(x\) terms: \[ 17x - 12x = 5x \]

3. Combine the constant terms: \[ 13 - 11 = 2 \]

Putting it all together, we have:

\[ 7x^2 + 5x + 2 \]

Thus, the simplified expression is:

\[ \boxed{7x^2 + 5x + 2} \]