Question

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

Answer 1

The area of a rectangle is given by the product of its length and its width. In this case, the length of the rectangle is k^2 + 3 and the width is k^2 + 7.

So, the area of the rectangle can be expressed as:

(k^2 + 3)(k^2 + 7)

To simplify this expression, we can use the distributive property:

k^2(k^2 + 7) + 3(k^2 + 7)

Expanding further:

k^4 + 7k^2 + 3k^2 + 21

Combining like terms:

k^4 + 10k^2 + 21

Therefore, the area of the entire rectangle is k^4 + 10k^2 + 21.