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Question
Factorize each of the following algebraic expression:
16 − a6 + 4a3b3 − 4b6
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Solution
\[16 - a^6 + 4 a^3 b^3 - 4 b^6 \]
\[ = 16 - ( a^6 - 4 a^3 b^3 + 4 b^6 )\]
\[ = 4^2 - [( a^3 )^2 - 2 \times a^3 \times 2 b^3 + (2 b^3 )^2 ]\]
\[ = 4^2 - ( a^3 - 2 b^3 )^2 \]
\[ = [4 - ( a^3 - 2 b^3 )][4 + ( a^3 - 2 b^3 )]\]
\[ = (4 - a^3 + 2 b^3 )(4 + a^3 - 2 b^3 )\]
\[ = ( a^3 - 2 b^3 + 4)( - a^3 + 2 b^3 + 4)\]
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