Question

use the distributive property to remove the parentheses.

\\4b^4(5 - 6b^5)\\

simplify your answer as much as possible.

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
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"concepts_used": [
"Exponent Rules"
],
"new_concepts": [
"Distributive Property",
"Multiplying Monomials"
],
"current_concepts": [
"Distributive Property",
"Exponent Rules",
"Multiplying Monomials"
]
}
</pre_analysis>

<reasoning>

Apply the distributive property

\[
4b^4(5 - 6b^5) = (4b^4 \cdot 5) - (4b^4 \cdot 6b^5)
\]

Simplify each term

\[

$$\begin{aligned} 4b^4 \cdot 5 &= 20b^4 \\ 4b^4 \cdot 6b^5 &= 24b^{4+5} = 24b^9 \end{aligned}$$

\]

Combine the simplified terms

\[
20b^4 - 24b^9
\]
</reasoning>

<answer>
Use the distributive property to remove the parentheses.
\(4b^4(5-6b^5)\)
Simplify your answer as much as possible.
<blank>\(20b^4 - 24b^9\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Distributive Property"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Exponent Rules"
],
"new_concepts": [
"Distributive Property",
"Multiplying Monomials"
],
"current_concepts": [
"Distributive Property",
"Exponent Rules",
"Multiplying Monomials"
]
}
</pre_analysis>

<reasoning>

Apply the distributive property

\[
4b^4(5 - 6b^5) = (4b^4 \cdot 5) - (4b^4 \cdot 6b^5)
\]

Simplify each term

\[

$$\begin{aligned} 4b^4 \cdot 5 &= 20b^4 \\ 4b^4 \cdot 6b^5 &= 24b^{4+5} = 24b^9 \end{aligned}$$

\]

Combine the simplified terms

\[
20b^4 - 24b^9
\]
</reasoning>

<answer>
Use the distributive property to remove the parentheses.
\(4b^4(5-6b^5)\)
Simplify your answer as much as possible.
<blank>\(20b^4 - 24b^9\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Distributive Property"
]
}
</post_analysis>