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Answer :
(i) Given:\(a^4 – b^4 \)
\(=(a^2)^2 – (b^2)^2\quad\)[∵ \(a^2 – b^2 = (a – b)(a + b)\)]
\(= (a^2 – b^2) (a^2 + b^2)\)
\(= (a – b) (a + b) (a^2 + b^2)\)
(ii) Given:\(p^4 – 81 = (p^2)^2 – (9)^2\)
\(= (p^2 – 9) (p^2 + 9)\quad\)[∵\( a^2 – b^2 = (a – b)(a + b)]\)
\(= (p – 3)(p + 3) (p^2 + 9)\)
(iii) Given:\(x^4 – (y + z)4 \)
\(= (x^2)^2 – [(y + z)^2]^2\quad\)[∵ \(a^2 – b^2 = (a – b)(a + b)\)]
\(= [x^2 – (y + z)^2] [x^2 + (y + z)^2]\)
\(= [x – (y + z)] [x + (y + z)] [x^2 + (y + z)^2]\)
\(= (x – y – z) (x + y + z) [x^2 + (y + z)^2]\)
(iv) Given:\(x^4 – (x – z)^4 = (x^2)^2 – [(y – z)^2]^2\)
\(= [x^2 – (y – z)^2] [x^2 + (y – z)^2]\)
\(= (x – y + z) (x + y – z) (x^2 + (y – z)^2]\)
(v)Given: \(a^4 – 2a^2b^2 + b^4\)
\(= a^4 – a^2b^2 – a^2b^2 + b^4\)
\(= a^2(a^2 – b^2) – b^2(a^2 – b^2)\)
\(= (a^2 – b^2)(a^2 – b^2)\)
\(= (a^2 – b^2)^2\)
\(= [(a – b) (a + b)]^2\)
\(= (a – b)^2 (a + b)^2\)