Question

x^4+4y^4 and 2x^3y+4xy6^3+4x^3+4X^2Y^2

Answer 1

Answer:

$1st = {x }^{2} + 4 {y}^{2} \\ = ( {x}^{2})^{2} + (2 {y}^{2})^{2} \\ = ({x}^{2} + 2 {y}^{2})^{2} - 2. {x}^{2} .2 {y}^{2} \\ = ( {x}^{2} + 2 {y}^{2} )^{2} - 4 {x}^{2} {y}^{2} \\ = ( {x}^{2} + 2 {y}^{2} )^{2} - (2x {y}^{2}){2} \\ = ( {x}^{2} + 2 {y }^{2} - 2xy)( {x}^{2} + 2 {y}^{2} + 2xy) \\ 2nd = (2 {x}^{3}y + 4x {y}^{3} + 4 {x}^{2} y) \\ = 2xy( {x}^{2} + 2 {y}^{2} + 2xy) \\ hcf \: = 2xy( {x}^{2} + 2 {y}^{2} + 2xy)$

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