Questions: Perform the indicated operation by removing the parentheses and combining like terms. [ (-3 x^2+9 x)+(-2 x^2+5 x+6) ]

Solution Steps

To solve this problem, we need to remove the parentheses and then combine the like terms. Like terms are terms that have the same variable raised to the same power. We will add the coefficients of the like terms together.

We start with the expression: \[ \left(-3 x^{2}+9 x\right)+\left(-2 x^{2}+5 x+6\right) \] Removing the parentheses, we rewrite it as: \[ -3 x^{2} + 9 x - 2 x^{2} + 5 x + 6 \]

Next, we combine the like terms. The like terms are:

• For \(x^{2}\): \(-3 x^{2} - 2 x^{2} = -5 x^{2}\)
• For \(x\): \(9 x + 5 x = 14 x\)
• The constant term is \(6\).

Thus, we have: \[ -5 x^{2} + 14 x + 6 \]

Final Answer