Which of the following is a factor of 500x³ + 108y¹⁸?
6, 5x + 3y⁶, 25x² + 15xy⁶ + 9y², all of the above

Solution:

Given 500x³ + 108y¹⁸

The given equation can be split into as follows: 4(125x³) + 4(27y¹⁸)(Taking out 4)

= 4(125x³ + 27y¹⁸)

= 4( (5x)³ + (3y⁶)³)

Using the algebraic identity, we have a³+b³ = (a + b) (a² - ab + b² )

here a= 5x and b=3y⁶

= 4{(5x+3y⁶)((5x)² - (5x)(3y⁶) + (3y⁶)²)}

= 4{(5x+3y⁶)(25x² - 15xy⁶ + 9y¹²)}

= 4(5x+3y⁶)(25x² - 15xy⁶ + 9y¹²)

Which of the following is a factor of 500x³ + 108y¹⁸?
6, 5x + 3y⁶, 25x² + 15xy⁶ + 9y², all of the above

Summary:

The following are the factors of 500x3 + 108y¹⁸ 4, (5x+3y⁶), (25x² - 15xy⁶ + 9y¹²).