Question

perform the indicated operation.
$(-2x^{3}+7x^{2}-10x + 3)+(9x^{3}+4x^{2}-8x - 7)$
write the polynomial in standard form.
$(-2x^{3}+7x^{2}-10x + 3)+(9x^{3}+4x^{2}-8x - 7)=\square$

Explanation:

Step1: Remove parentheses

To add the two polynomials, we first remove the parentheses. Since there is a plus sign in front of the second parentheses, the signs of the terms inside remain the same. So we have:
$-2x^{3}+7x^{2}-10x + 3+9x^{3}+4x^{2}-8x-7$

Step2: Combine like terms for $x^{3}$ terms

The terms with $x^{3}$ are $-2x^{3}$ and $9x^{3}$. Combining them:
$-2x^{3}+9x^{3}=(-2 + 9)x^{3}=7x^{3}$

Step3: Combine like terms for $x^{2}$ terms

The terms with $x^{2}$ are $7x^{2}$ and $4x^{2}$. Combining them:
$7x^{2}+4x^{2}=(7 + 4)x^{2}=11x^{2}$

Step4: Combine like terms for $x$ terms

The terms with $x$ are $-10x$ and $-8x$. Combining them:
$-10x-8x=(-10-8)x=-18x$

Step5: Combine constant terms

The constant terms are $3$ and $-7$. Combining them:
$3-7=-4$

Step6: Write in standard form

Now we put all the combined terms together in descending order of the exponents of $x$. So the polynomial in standard form is:
$7x^{3}+11x^{2}-18x - 4$

Answer:

$7x^{3}+11x^{2}-18x - 4$