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Svetllana [295]
3 years ago
5

Factorise a^4 -(a+b)^4

Mathematics
1 answer:
Flura [38]3 years ago
8 0

Step-by-step explanation:

{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 ) \\

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