To find (b-c)^6, we can first rewrite (b-c) as a variable, let's say, x.
So x = b - c
Then, we can rewrite the given equation in terms of x:
x^2 - 2bc + c^2 = 9
Now, we can substitute x back in terms of b and c:
x^2 = (b - c)^2= b^2 - 2bc + c^2
Therefore, x^2 = b^2 - 2bc + c^2
So, our equation becomes:
x^2 = 9
Now, to find (b-c)^6, we need to raise x to the power of 6:
x^6 = 9^3= 729
Therefore, (b-c)^6 = 729.
To find (b-c)^6, we can first rewrite (b-c) as a variable, let's say, x.
So x = b - c
Then, we can rewrite the given equation in terms of x:
x^2 - 2bc + c^2 = 9
Now, we can substitute x back in terms of b and c:
x^2 = (b - c)^2
= b^2 - 2bc + c^2
Therefore, x^2 = b^2 - 2bc + c^2
So, our equation becomes:
x^2 = 9
Now, to find (b-c)^6, we need to raise x to the power of 6:
x^6 = 9^3
= 729
Therefore, (b-c)^6 = 729.