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Question
Factorize each of the following expression:
a4 − 16b4
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Solution
\[a^4 - 16 b^4 = a^4 - 2^4 b^4 = ( a^2 )^2 - ( 2^2 b^2 )^2 \]
\[ = ( a^2 - 2^2 b^2 )( a^2 + 2^2 b^2 )\]
\[ = [ a^2 - (2b )^2 ]( a^2 + 4 b^2 )\]
\[ = (a - 2b)(a + 2b)( a^2 + 4 b^2 )\]
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