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Factorise. x^4 –(x–z)^4 ????????????????????????????????

Factorise.
 x^4 –(x–z)^4 ????????????????????????????????

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
2 years ago
Dear Student

x^4 –(x–z)^4
= (x^2)^2-{(x-z)^2}^2
= {x^2-(x-z)^2}{x^2+(x-z)^2}
= { x-(x-z)}{x+(x-z)} {x^2+(x-z)^2}
= z(2x-z)( x^2+x^2-2xz+z^2)
= z(2x-z)( 2x^2-2xz+z^2)

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