Question

multiply monomials by polynomials: area model 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. area =

Explanation:

Step1: Recall area formula

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

Step2: Apply distributive property

$A = 5m^{4}\times m^{2}-5m^{4}\times2m-5m^{4}\times1$.

Step3: Use exponent - rule $a^{m}\times a^{n}=a^{m + n}$

$5m^{4}\times m^{2}=5m^{4 + 2}=5m^{6}$, $5m^{4}\times2m = 10m^{4+1}=10m^{5}$, and $5m^{4}\times1 = 5m^{4}$.

Step4: Write in standard form

$A=5m^{6}-10m^{5}-5m^{4}$.

Answer:

$5m^{6}-10m^{5}-5m^{4}$