Question

factorise:x⁴-(x-z)⁴​

Answer 1

Step-by-step explanation:

x4-(x-z)4

x4-(x2-2xz+z2)2

x4 - (x4-2x3z+x2z2-2x3z+4x2z2-2xz3+x2z2-2xz3+z4)

Combine like terms

x4 - (x4-4x3z+6x2z2-4xz3+z4)

4x3z-6x2z2+4xz3-z4

Answer 2

Answer:

The factors of x⁴ - (x - z)⁴ is$[2x^{2}+z^{2}-2xz][2x-z]z$.

Step-by-step explanation:

Factorize the equation as follows:

$x^{4}-(x-z)^{4}=(x^{2})^{2}-[(x-z)^{2}]^{2}\\=[x^{2}+(x-z)^{2}][x^{2}-(x-z)^{2}]\\=[x^{2}+x^{2}+z^{2}-2xz][(x+(x-z)][x-(x-z)]\\=[2x^{2}+z^{2}-2xz][2x-z]z$

Thus, the factors of x⁴ - (x - z)⁴ is$[2x^{2}+z^{2}-2xz][2x-z]z$.