Question

Subtract.

Your answer should be a polynomial in standard form.
(-5v³-9v² +6v)-(-5v³ +9v² - 6v)

Answer 1

To combine like terms, we need to add the coefficients of the same variables. The given polynomial is actually the difference of two polynomials, so we need to add the coefficients of the same variables in each of the polynomials.

The polynomial $(-5v^3-9v^2+6v)$ has terms with coefficients $-5$, $-9$, and $6$ for the variables $v^3$, $v^2$, and $v$ respectively. The polynomial $(-5v^3+9v^2-6v)$ has terms with coefficients $-5$, $9$, and $-6$ for the variables $v^3$, $v^2$, and $v$ respectively.

The difference of the two polynomials is

\begin{align*}

(-5v^3-9v^2+6v)-(-5v^3+9v^2-6v) &= (-5v^3-9v^2+6v)+5v^3-9v^2+6v \

&= -5v^3+5v^3-9v^2+9v^2+6v-6v \

&= 0v^3+0v^2+0v+0 \

&= 0.

\end{align*}

Therefore, the difference of the two given polynomials is the constant polynomial $0$. In standard form, this is written as $\boxed{0}$.