Question

a rectangle has a height of $4w^3$ and a width of $5w^2 - 3w - 4$. express the area of the entire rectangle. your answer should be a polynomial in standard form.

Explanation:

Step1: Use the area formula of rectangle

The area formula of a rectangle is \(A = \text{height}\times\text{width}\). Here, height \(h = 4w^{3}\) and width \(w=5w^{2}-3w - 4\). So \(A=4w^{3}(5w^{2}-3w - 4)\).

Step2: Apply the distributive property

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

For \(4w^{3}\times5w^{2}\), we have \(4\times5\times w^{3 + 2}=20w^{5}\).
For \(4w^{3}\times3w\), we have \(4\times3\times w^{3+1}=12w^{4}\).
For \(4w^{3}\times4\), we have \(16w^{3}\).
So \(A = 20w^{5}-12w^{4}-16w^{3}\)

Answer:

\(20w^{5}-12w^{4}-16w^{3}\)