We are doing mathematical induction and the teacher gave us this example and I'm a little confused.

7^n - 3^n div. by 4
1) Base case: n=1
2)Induction Hypothesis
Need to show that it is true for n+1
7^(n+1) - 3^(n+1) div. by 4
7 * 7^n - 3 * 3^n
3(7^n - 3^n) + 4*7^n

I understand the concept of mathematical induction. The only part that I don't understand is how to get to the final step (from 7 * 7^n - 3 * 3^n to 3(7^n - 3^n) + 4*7^n). He tried to explain it using this: 7x - 3y = 3(x-y) + 4x

Anyone care to explain that part?

Question

We are doing mathematical induction and the teacher gave us this example and I'm a little confused.

7^n - 3^n div. by 4
1) Base case: n=1
2)Induction Hypothesis
Need to show that it is true for n+1
7^(n+1) - 3^(n+1) div. by 4
7 * 7^n - 3 * 3^n
3(7^n - 3^n) + 4*7^n

I understand the concept of mathematical induction. The only part that I don't understand is how to get to the final step (from 7 * 7^n - 3 * 3^n to 3(7^n - 3^n) + 4*7^n). He tried to explain it using this: 7x - 3y = 3(x-y) + 4x

Anyone care to explain that part?