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A day full of math games & activities. Find one near you.
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).
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