Question

factorise : x^4 -(y+z)^4​

Answer 1

Answer:

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Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\: \: \: \: \: \: \underline{ \bold { \: \: IDENTITY \: \: USED \: \: }} \\ \\ \sf{ \green{1. \: a {}^{2} - b {}^{2} = ( a + b)(a - b)}} \\ \\ \sf{ \green{2. \: (a + b) {}^{2} = a {}^{2} + 2ab + b {}^{2} }}$

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$\: \: \: \: \: \: \: \tt{ \red{x {}^{4} - (y + z) {}^{4}}} \\ \\ \tt{ \pink{= (x {}^{2}) {}^{2} - \{(y + z) {}^{2} \} {}^{2}}} \\ \\ \tt{ \blue{= \{x {}^{2} + (y + z) {}^{2} \} \{x {}^{2} - (y + z) {}^{2} \}}} \\ \\ \tt{ \pink{= \{x{}^{2} + (y {}^{2} + 2yz + z {}^{2} ) \}[ \{x + (y +z ) \} \{x - (y + z )\}] }} \\ \\ \tt{ \red{ = (x{}^{2} + y {}^{2} + z {}^{2} + 2yz ) (x+y+z) (x-y-z) }}$