Question

topic: operations with polynomials
progress
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
subtract: $(-2x^4 - 4y^3 + 4z^3 + 6) - (-9x^4 - 3y^3 + 4z^3 + 9)$
$\circ -11x^4 - 7y^3 + 8z^3 + 15$
$\circ 7x^4 - y^3 - 3$
$\circ -7x^4 + y^3 + 3$
$\circ -11x^4 - 7y^3 - 3$

Explanation:

Step1: Distribute the subtraction

We have to subtract the second polynomial from the first. So, we distribute the negative sign to each term in the second polynomial:
$$(-2x^4 - 4y^3 + 4z^3 + 6) - (-9x^4 - 3y^3 + 4z^3 + 9)$$
$$= -2x^4 - 4y^3 + 4z^3 + 6 + 9x^4 + 3y^3 - 4z^3 - 9$$

Step2: Combine like terms

• For \(x^4\) terms: \(-2x^4+9x^4 = 7x^4\)
• For \(y^3\) terms: \(-4y^3 + 3y^3=-y^3\)
• For \(z^3\) terms: \(4z^3-4z^3 = 0\)
• For constant terms: \(6 - 9=-3\)

Putting it all together, we get \(7x^4 - y^3 - 3\)

Answer:

\(7x^4 - y^3 - 3\) (corresponding to the third option)