Question

Factorize each of the following expression:
a⁴ − 16(b − c)⁴

Answer 1

\[a^4 - 16(b - c )^4 \]
\[ = ( a^2 )^2 - [4(b - c )^2 ]^2 \]
\[ = [ a^2 + 4(b - c )^2 ][ a^2 - 4(b - c )^2 ]\]
\[ = [ a^2 + 4(b - c )^2 ]{ a^2 - [2(b - c) ]^2 }\]
\[ = [ a^2 + 4(b - c )^2 ][a + 2(b - c)][a - 2(b - c)]\]
\[ = [ a^2 + 4(b - c )^2 ](a + 2b - 2c)(a - 2b + 2c)\]