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

Answer:

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

Step-by-step 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 $k^4 +10 k^2 + 21$