Question

a rectangle has a height of $5m^{4}$ and a width of $m^{2}-2m - 1$.
express the area of the entire rectangle.
your answer should be a polynomial in standard form.
$m^{2}+-2m+-1$
$5m^{4}$
area $=$

Explanation:

Step1: Use the area formula for a rectangle

The area formula for a rectangle is \(A = \text{height}\times\text{width}\). Here, the height \(h = 5m^{4}\) and the width \(w=m^{2}-2m - 1\). So, \(A=5m^{4}(m^{2}-2m - 1)\).

Step2: Apply the distributive property

$$
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$$

Step3: Use the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\)

For \(5m^{4}\times m^{2}\), we have \(5m^{4 + 2}=5m^{6}\). For \(5m^{4}\times2m\), we have \(10m^{4+1}=10m^{5}\). And \(5m^{4}\times1 = 5m^{4}\). So, \(A = 5m^{6}-10m^{5}-5m^{4}\).

Answer:

\(5m^{6}-10m^{5}-5m^{4}\)