Successive differences of perfect cubes eventually become equal at the third level. This shows that cubes grow at a rate where third-order differences are constant, which is why they’re called third-degree polynomials in algebra.
Class 8 NCERT Ganita Prakash Chapter 1 A Square and A Cube solutions
Class 8 Mathematics Textbook Chapter 1 A Square and A Cube question answer
When we calculate differences of perfect cubes, we do:
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125
First level: 7, 19, 37, 61
Second level: 12, 18, 24
Third level: 6, 6
The third-level differences are constant. This reveals that perfect cubes follow a third-degree pattern. So, the third successive differences of cubes are always equal.
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