a³ + 3ab(a + b) + b³ = ____?
- 3(a + b)³
- (a + b)³
- (3a + 3b)³
- None of these
Explanation
The given expression is:
a³ + 3ab(a + b) + b³
Factor the expression:
(a + b)(a² - ab + b²) + 3ab(a + b)
Combine like terms:
(a + b)(a² - ab + b² + 3ab)
Simplify:
(a + b)(a² + 2ab + b²)
Recognize the perfect cube:
(a + b)³
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