Question

Factorize: a (a + b)³ - 3a²b (a + b)

Answer 1

Taking (a + b) common in two terms

= (a + b){a (a + b)² - 3a²b}

Now, using (a + b)²  = a²  + b²  + 2ab

= (a + b){a (a² + b² + 2ab) - 3a²b}

= (a + b){a³ + ab² + 2a²b - 3a²b}

= (a + b){a³ + ab² - a²b}

= (a + b) a{a² + b² - ab}

= a (a + b)(a² + b² - ab)

∴ a (a + b)³ - 3a²b (a + b) = a (a + b)(a² + b² - ab)