Question

PLEASE HELP ME WITH THIS MATH PROBLEM!!

Answer 1

Given : The Area of the Rectangle = x⁴ - 100

We know that : (a + b)(a - b) = a² - b²

⇒   x⁴ - 100 can be written as : (x²)² - (10)²

⇒   (x²)² - (10)² can be written as : (x² + 10)(x² - 10)

We know that, Area of a Rectangle is given by : Length × Width

Comparing (x² + 10)(x² - 10) with Area of the Rectangle formula, We can notice that :

⊕   Length = x² + 10

⊕   Width = x² - 10

Given : Length of the Rectangle is 20 units more than Width

⇒   Width + 20 = Length

⇒   x² - 10 + 20 = x² + 10

⇒   x² + 10 = x² + 10

Answer : x² - 10 represents the width of the rectangle. Because the area expression can be rewritten as (x² - 10)(x² + 10) which equals

(x² - 10)((x² - 10) + 20)

⇒   Option A