Question $\begin{aligned} 4 p^{5}(v-4)(9 v-1) & =4 p^{5}\left(9 v^{2}-v-36 v+4\right) \\ & =4 p^{5}\left(9 v^{2}-\square v+4\right)\end{aligned}$

Studdy Solution

STEP 1

1. The expression involves polynomial multiplication and simplification.
2. We need to find the correct coefficient for $v$ in the expanded form.

STEP 2

1. Expand the expression $(v-4)(9v-1)$ .
2. Simplify the expanded expression to identify the coefficient of $v$ .

STEP 3

Expand the expression $(v-4)(9v-1)$ using the distributive property (FOIL method):
First: $v \times 9v = 9v^2$
Outer: $v \times (-1) = -v$
Inner: $-4 \times 9v = -36v$
Last: $-4 \times (-1) = 4$
Combine these results:
$9v^2 - v - 36v + 4$

STEP 4

Combine like terms to simplify the expression:
Combine the terms with $v$ :
$-v - 36v = -37v$
So, the expression becomes:
$9v^2 - 37v + 4$
Therefore, the coefficient of $v$ is $-37$ .
The completed expression is:
$4p^5(9v^2 - 37v + 4)$

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