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Factorise.

(i) a4 – b4

(ii) p4 – 81

(iii) x4 – (y + z)4

(iv) x4 – (x – z)4

(v) a4 – 2a²b² + b4

1 Answer

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(i) a4 – b4

Answer: a4-b4 = (a²+b²)(a²-b²)

(ii) p4 – 81
=(p²+9)(p²-9)

(iii) x4 – (y + z)4

Answer: x4 – (y + z)4
= (x²+(y+z) ²)(x²-(y+z) ²)
= (x²+(y+z)²)[(x+y+z)(x-y-z)]

(iv) x4 – (x – z)4

Answer: x4 – (x – z)4
=(x²-(x-z) ²)(x²+(x-z) ²)
=[(x+x-z)(x-x+z)](x²+(x-z) ²]

(v) a4 – 2a²b² + b4

Answer: a4 – 2a2b2 + b4
This can be factorised by using the identity; (a - b)2 = a2 – 2ab + b2
Factors = (a2 – b2)2 = (a2 – b2)(a2 – b2)

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