Question

unit: exponents and polynomials
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
a rectangular prism has the following dimensions: ( l = 5a ), ( w = 2a ), and ( h = (a^3 - 3a^2 + a) ). use the formula ( v = l cdot w cdot h ) to find the volume of the rectangular prism.
( 10a^5 - 3a^2 + a )
( 10a^5 - 30a^4 + 10a^3 )
( 10a^6 - 30a^4 + 10a^2 )
( 10a^4 - 30a^3 + 10a^2 )
question id: 98267

Explanation:

Step1: Recall the volume formula

The volume \( V \) of a rectangular prism is given by \( V = l \cdot w \cdot h \). We know \( l = 5a \), \( w = 2a \), and \( h = a^3 - 3a^2 + a \). First, multiply \( l \) and \( w \): \( 5a \cdot 2a = 10a^2 \).

Step2: Multiply by the height

Now, multiply \( 10a^2 \) by \( (a^3 - 3a^2 + a) \) using the distributive property (also known as the distributive law of multiplication over addition).

$$
LATEXBLOCK0
$$

Answer:

\( 10a^5 - 30a^4 + 10a^3 \) (which corresponds to the third option: \( 10a^5 - 30a^4 + 10a^3 \))