Step-by-step explanation:
[tex] {a}^{4} - (a + b)^{4} \\ = ( {a}^{2})^{2} - \{ (a + b)^{2} \}^{2} \\ = \{ {a}^{2} - (a + b)^{2} \}\{ {a}^{2} + (a + b)^{2} \} \\ = \{ {a} + (a + b) \}\ \: \{ {a} - (a + b) \}\{ {a}^{2} + (a + b)^{2} \} \\ = \{ {a} + a + b \}\ \: \{ {a} - a - b\}\{ {a}^{2} + a^{2} + b^{2} + 2ab\} \\ = (2a + b)( - b)(2 {a}^{2} + {b}^{2} + 2ab ) \\ = - b(2a + b)(2 {a}^{2} + {b}^{2} + 2ab ) \\ [/tex]
