If a - b = 10 and ab = 4, then the value of a3- b3 + 4(a + b)2 is:
1584
The correct answer is 1584.
Understanding these identities is crucial for simplifying expressions, solving equations, and working with polynomials. The ability to derive one identity from another (like finding $\small a^2+b^2$ from $\small (a-b)^2$ and $\small ab$) is a key skill. Problems like this demonstrate how knowing a few basic relationships can help solve more complex expressions. Practice with various identities improves algebraic fluency and problem-solving speed.
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