Question

A rectangle has a height of k2 + 3 and a width of k2 + 7.

Express the area of the entire rectangle.

Your answer should be a polynomial in standard form.

k2

2

+

Answer 1

The area of the rectangle in polynomial form is
`k^4 +10 k^2 + 21`

Explanation:

Given

Shape: Rectangle

`Height: k^2 + 3`

`Width: k^2 + 7`

Required

Area of the rectangle

The area of a rectangle is calculated as thus;

`Area = Length * Width`

By substituting
`k^2 + 3` for height and
`k^2 + 7` for width; This gives

`Area = (k^2 + 3)(k^2 + 7)`

Expand the bracket

`Area = k^2(k^2 + 7) + 3(k^2 + 7)`

Open each bracket

`Area = k^2*k^2 + k^2*7 + 3*k^2 + 3*7`

`Area = k^4 +7 k^2 + 3k^2 + 21`

`Area = k^4 +10 k^2 + 21`

Hence, the area of the rectangle in polynomial form is
`k^4 +10 k^2 + 21`