Factorise.(i) a4 – b4(ii) p4 – 81(iii) x4 – (y + z)4(iv) x4

1.	Factorise.(i) a4 – b4(ii) p4 – 81(iii) x4 – (y + z)4(iv) x4 – (x – z)4(v) a4 – 2a²b² + b4
Answer» (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)

Factorise.(i) a4 – b4(ii) p4 – 81(iii) x4 – (y + z)4(iv) x4 – (x – z)4(v) a4 – 2a²b² + b4

Answer»

(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)