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aleksandr82 [10.1K]
3 years ago
11

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

Mathematics
2 answers:
attashe74 [19]3 years ago
7 0

Answer:

<h2>x2−10 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2−10)+20).</h2>

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.

nadezda [96]3 years ago
4 0

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.

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