Consider the difference pattern of cubes: 2^3 - 1^3 = 7 3^3 - 2^3 = 19 The difference n^3 - (n-1)^3 always equals 3n^2 - 3n + 1. Using this, what is 7^3 - 6^3?

Question

Accepted Answer

127. Using 3n^2 - 3n + 1 with n = 7: 3(49) - 21 + 1 = 147 - 21 + 1 = 127. Check: 343 - 216 = 127.

Consider the difference pattern of cubes:
$2^{3} - 1^{3} = 7 3^{3} - 2^{3} = 19$
The difference $n^{3} - (n - 1)^{3}$ always equals $3 n^{2} - 3 n + 1$ .
Using this, what is $7^{3} - 6^{3}$ ?

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More Class 8 Patterns in Cubes practice

Consider the difference pattern of cubes:23−13=733−23=19The difference n3−(n−1)3 always equals 3n2−3n+1.Using this, what is 73−63?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Patterns in Cubes practice

Consider the difference pattern of cubes:
$2^{3} - 1^{3} = 7 3^{3} - 2^{3} = 19$
The difference $n^{3} - (n - 1)^{3}$ always equals $3 n^{2} - 3 n + 1$ .
Using this, what is $7^{3} - 6^{3}$ ?