Question

use the distributive property to remove the parentheses.

\\((6x^3 - 5x^2 + 8)9x^4\\)

simplify your answer as much as possible.

Explanation:

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<reasoning>

Apply the distributive property

\[
(6x^3 - 5x^2 + 8) \cdot 9x^4 = (6x^3 \cdot 9x^4) - (5x^2 \cdot 9x^4) + (8 \cdot 9x^4)
\]

Multiply the monomials

\[

$$\begin{aligned} 6x^3 \cdot 9x^4 &= 54x^{3+4} = 54x^7 \\ 5x^2 \cdot 9x^4 &= 45x^{2+4} = 45x^6 \\ 8 \cdot 9x^4 &= 72x^4 \end{aligned}$$

\]

Combine the terms

\[
54x^7 - 45x^6 + 72x^4
\]
</reasoning>

<answer>
Use the distributive property to remove the parentheses.
\[ (6x^3 - 5x^2 + 8)9x^4 \]
Simplify your answer as much as possible.
<blank>\(54x^7 - 45x^6 + 72x^4\)</blank>
</answer>

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"Mathematics",
"Algebra",
"Polynomial Multiplication"
]
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</post_analysis>

Answer:

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<reasoning>

Apply the distributive property

\[
(6x^3 - 5x^2 + 8) \cdot 9x^4 = (6x^3 \cdot 9x^4) - (5x^2 \cdot 9x^4) + (8 \cdot 9x^4)
\]

Multiply the monomials

\[

$$\begin{aligned} 6x^3 \cdot 9x^4 &= 54x^{3+4} = 54x^7 \\ 5x^2 \cdot 9x^4 &= 45x^{2+4} = 45x^6 \\ 8 \cdot 9x^4 &= 72x^4 \end{aligned}$$

\]

Combine the terms

\[
54x^7 - 45x^6 + 72x^4
\]
</reasoning>

<answer>
Use the distributive property to remove the parentheses.
\[ (6x^3 - 5x^2 + 8)9x^4 \]
Simplify your answer as much as possible.
<blank>\(54x^7 - 45x^6 + 72x^4\)</blank>
</answer>

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"Mathematics",
"Algebra",
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</post_analysis>