Question

(2x + 3y)

$(2x + 3y) {}^{2}$
​

Answer 1

Given:-

$(2x + 3y)(2x + 3y) ^{2}$

$(2x + 3y)(2x - 3y)(2x - 3y)$

Distribute:-

$(2x + 3y)(2x - 3y)(2x - 3y)$

$(2x - 3y)(2x(2x - 3y) - 3y(2x - 3y)$

$(2x - 3y)( {4x}^{2} - 6xy - 3y(2x - 3y)$

$(2x + 3y)( {4x}^{2} - 6xy - 6xy + 9y ^{2} )$

$(2x - 3y)( {4x}^{2} - 6xy - 6xy + 9y ^{2} )$

$(2x + 3y)( {4x}^{2} - 12xy + 9y ^{2} )$

$(2x + 3y)( {4x}^{2} - 12xy + {9y}^{2} )$

$2x( {4x}^{2} - 12xy + {9y}^{2} ) + 3y( {4x}^{2} - 12xy + {9y}^{2} )$

$2x( {4x}^{2} - 12xy + {9y}^{2} ) + 3y( {4x}^{2} - 12xy + {9y}^{2} )$

${8x}^{3} - 24 {yx}^{2} + 18 {xy}^{2} + {3y}( {4x}^{2} - 12xy + {9y}^{2} )$

${8x}^{3} - 24yx ^{2} + 3y( {4x}^{2} - 12xy + {9y}^{2} )$

${8x}^{3} + 18 {y}^{3} - 24 {yx}^{2} + 3y( {4x}^{2} - 12xy + {9y}^{2} )$

${8x}^{3} + 18 {xy}^{2} - 24 {yx}^{2} + 3y( {4x}^{2} - 12xy + {9y}^{2} )$

${8x}^{3} + 18 {xy}^{2} - 24 {yx}^{2} - 36 {xy}^{2} + 27 {y}^{3}$

${8x}^{3} + 18 {xy}^{2} - 24 {yx}^{2} + 12 {yx}^{2} - 36 {xy}^{2} + 27 {y}^{3}$

Solution:-

${8x}^{3} - 18 {xy}^{2} + 27 {xy}^{3} - 12 {yx}^{2}$