Question

Multiply binomials by polynomials: area model Your answer should be a polynomial in standard form.2m^3+m^2+ 3m+m+8Area =

Answer 1

Explanation:

The area represented by the model can be written in terms of monomials as

`(2m^3+m^2+3m)(m+8)`

We expand the above expression to get:

`m(2m^3+m^2+3m)+8(2m^3+m^2+3m)`
`2m^4+m^3+3m^2+16m^3+8m^2+24m^{}`

Adding the like terms gives

`2m^4+(m^3+16m^3)+(3m^2+8m^2)+24m`
`\boxed{=2m^4+17m^3+11m^2+24m\text{.}}`

Hence, the area of the rectangle is

`\boxed{A=2m^4+17m^3+11m^2+24m\text{.}}`