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Question
Factorize each of the following expression:
a4b4 − 81c4
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Solution
\[a^4 b^4 - 81 c^4 \]
\[ = ( a^2 b^2 )^2 - (9 c^2 )^2 \]
\[ = ( a^2 b^2 + 9 c^2 )( a^2 b^2 - 9 c^2 )\]
\[ = ( a^2 b^2 + 9 c^2 )[(ab )^2 - (3c )^2 ]\]
\[ = ( a^2 b^2 + 9 c^2 )(ab + 3c)(ab - 3c)\]
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