Question

simplify the following expression.

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

\\25h^{?} + \quadh^4 + \quadh^{\quad}\\

Explanation:

Apply the distributive property

Using the Distributive Property knowledge point

$$ 5h^3(5h^2 - h - 3) = (5h^3 \cdot 5h^2) + (5h^3 \cdot (-h)) + (5h^3 \cdot (-3)) $$

Simplify each term using exponent rules

Using the Product Rule of Exponents knowledge point

$$
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$$

Combine the simplified terms

We write the final expanded expression by combining the simplified terms:

$$ 25h^5 - 5h^4 - 15h^3 $$

To match the requested format \(25h^{[?]} + [ ]h^4 + [ ]h^{[ ]}\), we express subtraction as adding negative coefficients:

$$ 25h^5 + (-5)h^4 + (-15)h^3 $$

Comparing this to the template, the missing values are:

• First exponent: \(5\)
• Second coefficient: \(-5\)
• Third coefficient: \(-15\)
• Third exponent: \(3\)

Answer:

Simplify the following expression.
\(5h^3(5h^2 - h - 3)\)
\(25h^{\text{5}} + \text{-5}h^4 + \text{-15}h^{\text{3}}\)