Questions: A rectangle has a height of 3p^2+1 and a width of p^3+4. Express the area of the entire rectangle. Your answer should be a polynomial in standard form. Area =

A rectangle has a height of 3p^2+1 and a width of p^3+4.

Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.

Area =

Transcript text: A rectangle has a height of $3 p^{2}+1$ and a width of $p^{3}+4$. Express the area of the entire rectangle. Your answer should be a polynomial in standard form. Area $=$ $\square$

Solution

Express the area of the entire rectangle.

Find the area of the rectangle.

The area of a rectangle is given by $ \text{Area} = \text{height} \times \text{width} $. Given that the height is $ 3p^2 + 1 $ and the width is $ p^3 + 4 $, the area is:

Area $ = (3p^2 + 1)(p^3 + 4) $

Expand the expression.

$ (3p^2 + 1)(p^3 + 4) = 3p^2(p^3) + 3p^2(4) + 1(p^3) + 1(4) $ $ = 3p^5 + 12p^2 + p^3 + 4 $

Write the polynomial in standard form.

$ 3p^5 + p^3 + 12p^2 + 4 $

$ \boxed{3p^5 + p^3 + 12p^2 + 4} $

$ 3p^5 + p^3 + 12p^2 + 4 $

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