Question

The length of a rectangle is 20 units more than its width. The area of the rectangle is x4−100.

Answer 1

Answer:

x2−10 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2−10)+20).

Step-by-step explanation:

The area of the rectangle is $x^{4} -100$, which can be factored as $(x^{2} +10)(x^{2} -10)$, because it's the difference of two perfect squares.

But, we know that $l=20+w$, where $l$ is the length and $w$ is the width.

Additionally, $l=x^{2} -10+20$ and $w=x^{2} -10$, which means $l=x^{2} +10$.

Therefore, the right answer is A.

Answer 2

Answer:

$1. x^2-10$ because the area expression can be rewritten as $(x^2-10)(x^2+10)$which equals $(x^2-10)((x^2-10)+20).$

Step-by-step explanation:

Area of the rectangle $=(x^4-100)$

$x^4-100=(x^2)^2-10^2\\ Applying difference of two squares: a^2-b^2=(a-b)(a+b)\\(x^2)^2-10^2=(x^2-10)(x^2+10)$

Since the length of a rectangle is 20 units more than its width.

$Width: x^2-10\\Length=x^2+10=x^2-10+20$

The correct option is therefore 1.