Questions: -5wx^3(4w^2-9w^4x^5+3x^5)

Transcript text: $-5 w x^{3}\left(4 w^{2}-9 w^{4} x^{5}+3 x^{5}\right)$

Solution

Solution Steps

To simplify the given expression, we need to distribute the term $-5wx^3$ across each term inside the parentheses. This involves multiplying $-5wx^3$ by each term in the expression $4w^2$, $-9w^4x^5$, and $3x^5$. After distributing, we combine like terms if possible.

Step 1: Distributing the Expression

We start with the expression $ -5wx^3(4w^2 - 9w^4x^5 + 3x^5) $. To simplify, we distribute $ -5wx^3 $ across each term inside the parentheses:

\[ -5wx^3 \cdot 4w^2 = -20w^3x^3 \] \[ -5wx^3 \cdot (-9w^4x^5) = 45w^5x^8 \] \[ -5wx^3 \cdot 3x^5 = -15wx^8 \]

Step 2: Combining Like Terms

After distributing, we combine the results:

\[ -20w^3x^3 + 45w^5x^8 - 15wx^8 \]

Step 3: Final Simplified Expression

The final simplified expression is:

\[ 45w^5x^8 - 20w^3x^3 - 15wx^8 \]