(i) 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})

(ii) a^{4} − 2a^{2}b^{2 }+ b^{4}

= (a^{2})^{2} − 2 (a^{2}) (b^{2}) + (b^{2})^{2}

= (a^{2} − b^{2})^{2}

= [(a − b) (a + b)]^{2}

= (a − b)^{2} (a + b)^{2}