factorize 25x^4+4x^2y^2+4y^4
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Solution :
25x⁴ + 4x²y² + 4y⁴
= ( 5x² )² + 2*5x²*2y² + ( 2y² )² - 16x²y²
= ( 5x² + 2y² )² - ( 4xy )²
= ( 5x² + 2y² + 4xy )( 5x² + 2y² - 4xy )
•••••
25x⁴ + 4x²y² + 4y⁴
= ( 5x² )² + 2*5x²*2y² + ( 2y² )² - 16x²y²
= ( 5x² + 2y² )² - ( 4xy )²
= ( 5x² + 2y² + 4xy )( 5x² + 2y² - 4xy )
•••••
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