Question

simplify the following expression.

\\5h^3(5h^2 - h - 3)\\

\\25h^5 - 5h^4 - 15h^{?}\\

Explanation:

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<reasoning>

Apply the distributive property

Using the Distributive Property and Multiplying Monomials and Polynomials knowledge points
\[
5h^3(5h^2 - h - 3) = (5h^3 \cdot 5h^2) + (5h^3 \cdot (-h)) + (5h^3 \cdot (-3))
\]

Multiply the individual terms

Using the Product Rule of Exponents knowledge point
\[

$$\begin{aligned} 5h^3 \cdot 5h^2 &= 25h^{3+2} = 25h^5 \\ 5h^3 \cdot (-h^1) &= -5h^{3+1} = -5h^4 \\ 5h^3 \cdot (-3) &= -15h^3 \end{aligned}$$

\]

Combine the simplified terms

Combine the terms to write the final simplified expression:
\[
25h^5 - 5h^4 - 15h^3
\]
Comparing this result to the given expression \(25h^5 - 5h^4 - 15h^{[?]}\), the missing exponent is \(3\).
</reasoning>

<answer>
Simplify the following expression.
\[5h^3(5h^2 - h - 3)\]
\[25h^5 - 5h^4 - 15h^{\text{3}}\]
</answer>

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Answer:

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<reasoning>

Apply the distributive property

Using the Distributive Property and Multiplying Monomials and Polynomials knowledge points
\[
5h^3(5h^2 - h - 3) = (5h^3 \cdot 5h^2) + (5h^3 \cdot (-h)) + (5h^3 \cdot (-3))
\]

Multiply the individual terms

Using the Product Rule of Exponents knowledge point
\[

$$\begin{aligned} 5h^3 \cdot 5h^2 &= 25h^{3+2} = 25h^5 \\ 5h^3 \cdot (-h^1) &= -5h^{3+1} = -5h^4 \\ 5h^3 \cdot (-3) &= -15h^3 \end{aligned}$$

\]

Combine the simplified terms

Combine the terms to write the final simplified expression:
\[
25h^5 - 5h^4 - 15h^3
\]
Comparing this result to the given expression \(25h^5 - 5h^4 - 15h^{[?]}\), the missing exponent is \(3\).
</reasoning>

<answer>
Simplify the following expression.
\[5h^3(5h^2 - h - 3)\]
\[25h^5 - 5h^4 - 15h^{\text{3}}\]
</answer>

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