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Question
Factorize each of the following algebraic expression:
4x4 + y4
Solution
\[4 x^4 + y^4 \]
\[ = 4 x^4 + 4 x^2 y^2 + y^4 - 4 x^2 y^2 \]
\[ = [(2 x^2 )^2 + 2 \times 2 x^2 \times y + ( y^2 )^2 ] - (2xy )^2 \]
\[ = (2 x^2 + y^2 )^2 - (2xy )^2 \]
\[ = [(2 x^2 + y^2 ) - 2xy][(2 x^2 + y^2 ) + 2xy]\]
\[ = (2 x^2 - 2xy + y^2 )(2 x^2 + 2xy + y^2 )\]
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