Question

question 1 of 2
select the correct answer.
simplify the expression below.
$(-3x^2 + 2x - 4) + (4x^2 + 5x + 9)$
$\circ$ $x^2 + 7x + 13$
$\circ$ $x^2 + 11x + 1$
$\circ$ $7x^2 + 7x + 5$
$\circ$ $x^2 + 7x + 5$

Explanation:

Step1: Remove parentheses

To simplify the expression \((-3x^{2}+2x - 4)+(4x^{2}+5x + 9)\), we first remove the parentheses. Since there is a plus sign in front of both parentheses, the signs of the terms inside remain the same. So we get \(-3x^{2}+2x - 4+4x^{2}+5x + 9\).

Step2: Combine like terms (for \(x^{2}\) terms)

Next, we combine the like terms. For the \(x^{2}\) terms, we have \(-3x^{2}\) and \(4x^{2}\). Combining these, we use the rule of adding coefficients: \(-3x^{2}+4x^{2}=(-3 + 4)x^{2}=x^{2}\).

Step3: Combine like terms (for \(x\) terms)

For the \(x\) terms, we have \(2x\) and \(5x\). Combining these, we add their coefficients: \(2x+5x=(2 + 5)x = 7x\).

Step4: Combine like terms (for constant terms)

For the constant terms, we have \(-4\) and \(9\). Combining these, we get \(-4 + 9=5\).

Step5: Combine all combined terms

Now we put together the combined terms from the previous steps. So we have \(x^{2}+7x + 5\).

Answer:

\(x^{2}+7x + 5\) (which corresponds to the option: \(x^{2}+7x + 5\))