Question

A rectangle has a height of 5y^3 and a width of 3y^3-8y^2+2y. Express the area of the entire rectangle. Your answer should be a polynomial in standard form.

Answer 1

The area of entire rectangle in standard form is:
`15y^6 -40y^5 + 10y^4`

Solution:

Given that, A rectangle has:

`height = 5y^3 \\\\width = 3y^3 - 8y^2 + 2y`

Express the area of the entire rectangle

`\text{Area of rectangle } = 5y^3 * (3y^3 - 8y^2 + 2y)`

`Area = 5y^3* \:3y^3+5y^3\left(-8y^2\right)+5y^3* \:2y\\\\Area = 15y^6 -40y^5 + 10y^4 \\\\`

Standard form means that the terms are ordered from greatest exponent to lowest exponent

Thus area of entire rectangle in standard form is:
`15y^6 -40y^5 + 10y^4`