Question

A rectangle has a height of k^2+3k 2 +3k, squared, plus, 3 and a width of k^2+7k 2 +7k, squared, plus, 7. Express the area of the entire rectangle. Your answer should be a polynomial in standard form.

Answer 1

Answer: $k^4+10k^3+21k^2$

Step-by-step explanation:

Given

Height of rectangle is $h=k^2+3k$

Width is $w=k^2+7k$

The area of the rectangle is given by the multiplication of the height and width

$\Rightarrow A=\left(k^2+3k\right)\left(k^2+7k\right)\\\\\Rightarrow A=k^2k^2+k^2\cdot \:7k+3kk^2+3k\cdot \:7k\\\\\Rightarrow A=k^4+10k^3+21k^2$

Thus, the area of the rectangle is $k^4+10k^3+21k^2$.