Question

factorise
${x}^{4} - {(y + x)}^{4}$

Answer 1

$(x^{2})^2 -((y+x)^{2})^2 \\\\x^{2} -(y+x)^{2}$

Answer 2

Answer:

Step-by-step explanation:

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We know the algebraic identity:

a² - b² = ( a - b )( a + b )

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Here ,

x⁴ - ( y + x )⁴

= ( x² )² - [ ( y + x )² ]²

= [ x² - ( y + x )² ][ x² + ( y + x )²]

= {[x -( y + x )][x+(y+x)]}[x²+y²+x²+2xy]

= [ (x-y-x)(2x+y)][2x²+y²+2xy]

= (-y)(2x+y)(2x²+y²+2xy)

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