Explanation:
To find the value of (a^3 - b^3) / b^3 given that a/b = 7/3, you can use the formula for the difference of cubes:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
First, find the value of a - b using a/b = 7/3:
a/b = 7/3
Cross-multiply:
3a = 7b
Now, solve for a - b:
a - b = (3a - 7b)/3
Next, square the values of a and b:
a^2 = (a^2)
b^2 = (b^2)
Now, add ab to both sides:
ab = (ab)
Now, you can use the difference of cubes formula:
(a^3 - b^3) = (a - b)(a^2 + ab + b^2)
Plug in the values:
(a^3 - b^3) = [(3a - 7b)/3][(a^2 + ab + b^2)]
Now, divide the entire expression by b^3:
[(a^3 - b^3) / b^3] = [(3a - 7b)/3][(a^2 + ab + b^2)] / b^3
Simplify further if needed, but this is the expression for (a^3 - b^3) / b^3 given a/b = 7/3.