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

Which expression represents the width of the rectangle?

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

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

3. x2−30 because the area expression can be rewritten as (x2+10)(x2−10) which equals (x2+10)((x2−30)+20).

4. x2+30 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2+30)−20).

Respuesta :

Answer:

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

Step-by-step explanation:

Area of the rectangle [tex]=(x^4-100)[/tex]

[tex]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)[/tex]

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

[tex]Width: x^2-10\\Length=x^2+10=x^2-10+20[/tex]

The correct option is therefore 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 [tex]x^{4} -100[/tex], which can be factored as [tex](x^{2} +10)(x^{2} -10)[/tex], because it's the difference of two perfect squares.

But, we know that [tex]l=20+w[/tex], where [tex]l[/tex] is the length and [tex]w[/tex] is the width.

Additionally, [tex]l=x^{2} -10+20[/tex] and [tex]w=x^{2} -10[/tex], which means [tex]l=x^{2} +10[/tex].

Therefore, the right answer is A.

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