Question

X4-4 x square y square+4y4

Answer 1

$Given \: x^{4} - 4x^{2}y^{2} + 4y^{4} \\= (x^{2})^{2} - 2 \times x^{2} \times (2y^{2}) + (2y^{2})^{2} \\= ( x^{2} - 2y^{2} )^{2}$

/* By Algebraic Identity */

• a² - 2ab + b² = ( a - b )²

$= ( x^{2} - 2y^{2} )( x^{2} - 2y^{2} )$

Therefore.,

$\red {x^{4} - 4x^{2}y^{2} + 4y^{4}}\\ \green { = ( x^{2} - 2y^{2} )( x^{2} - 2y^{2} )}$

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