Rewrite in simplest terms: -10(9v - 4) + 10v.

Step-by-step solution

1. 1

   Distribute the $-10$ over both terms inside the bracket. The negative factor changes the sign of everything it multiplies:

   $-10(9v)=-90v,\qquad -10(-4)=+40$

   The second product is the one to watch: negative times negative gives $+40$, not $-40$.

2. 2

   Rewrite the expression bracket-free.

   $-90v+40+10v$

3. 3

   Collect the $v$ terms. Both coefficients are attached to the same variable, so they simply add:

   $-90v+10v=-80v$

4. 4

   Write the simplified expression.

   $-80v+40$

   If a fully factored form is wanted, both coefficients share a factor of $40$: $-80v+40=40(1-2v)$, or equivalently $-40(2v-1)$.

5. 5

   Check numerically. At $v=1$: the original is $-10(5)+10=-40$, and $-80(1)+40=-40\;\checkmark$. At $v=0$: the original is $-10(-4)+0=40$, and the simplified form gives $40\;\checkmark$, which pins down the constant term independently of the coefficient.