What will be the value of `a^3 + b^3 `, if `a^2 + b^2 = 32` and a + b = 8?

Options

A. 8
B. 32
C. 128
D. 256

Explanation

To find the value of \( a^3 + b^3 \) given that \( a^2 + b^2 = 32 \) and \( a + b = 8 \), we can use the following formulas:

1. The identity for the sum of cubes:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]

2. The relationship between \( a^2 + b^2 \) and \( (a + b)^2 \):
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