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प्रश्न
Factorize each of the following expression:
a4 − 16(b − c)4
उत्तर
\[a^4 - 16(b - c )^4 \]
\[ = ( a^2 )^2 - [4(b - c )^2 ]^2 \]
\[ = [ a^2 + 4(b - c )^2 ][ a^2 - 4(b - c )^2 ]\]
\[ = [ a^2 + 4(b - c )^2 ]{ a^2 - [2(b - c) ]^2 }\]
\[ = [ a^2 + 4(b - c )^2 ][a + 2(b - c)][a - 2(b - c)]\]
\[ = [ a^2 + 4(b - c )^2 ](a + 2b - 2c)(a - 2b + 2c)\]
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