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Solve the question :

(i) a4 − b4

(ii) p4 − 81

(iii) x4 − (y + z)4

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(i) a4 − b4 = (a2)2 − (b2)2

= (a2 − b2) (a2 + b2)

= (a − b) (a + b) (a2 + b2

(ii) p4 − 81  = (p2)2 − (9)2

= (p2 − 9) (p2 + 9)

= [(p)2 − (3)2] (p2 + 9)

= (p − 3) (p + 3) (p2 + 9)

(iii) x4 − (y + z)4 = (x2)2 − [(y +z)2]2

= [x2 − (y + z)2] [x2 + (y + z)2]

= [x − (y + z)][ x + (y + z)] [x2 + (y + z)2]

= (x − y − z) (x + y + z) [x2 + (y + z)2]

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