1.

X4-4 x square y square+4y4

Answer»

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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