An odd number cubed is an odd number.
To answer the question, we need to know what odd numbers are
What are odd numbers?
Odd numbers include 1,3, 5,7... and take the general for (2n + 1) where n = 0, 1, 2...
Now, we need to show that an odd number cubed is an odd number.
So, the odd number (2n + 1) cubed is
(2n + 1)³ = (2n + 1)(2n + 1)²
= (2n + 1)(4n² + 4n + 1)
= 8n³ + 8n² + 2n + 4n² + 4n + 1
= 8n³ + 12n² + 6n + 1
= 2(4n³ + 6n² + 3n) + 1
Since (4n³ + 6n² + 3n) is an integer say k, we have that
2(4n³ + 6n² + 3n) + 1 = 2k + 1
Since 2k + 1 is an odd number, 2n + 1 is an odd number and (2n + 1)³ = 2k + 1 which is an odd number.
So, an odd number cubed is an odd number.
Learn more about odd numbers here:
https://brainly.com/question/15490594
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