Factorise the following:(i) x4 – y4(ii) a4 – (b + c)4(iii) l2 �

1.	Factorise the following:(i) x4 – y4(ii) a4 – (b + c)4(iii) l2 – (m – n)2
Answer» (i) x⁴– y⁴ = (x²)² – (y²)² is in the form of a² – b² a² – b² = (a + b) (a – b) x⁴ – y⁴ = (x² + y²)(x² – y²) = (x² + y²)(x + y)(x – y) (ii) a⁴ – (b + c)⁴ a⁴ – (b + c)⁴ = (a²)² – [(b + c)²]² = [a² + (b + c)²] [a² – (b + c)²] , = [a² + (b + c)²] (a + b + c) [a – (b + c)] = [a² + (b + c)²] (a + b + c) (a – b – c) (iii) l² – (m – n)² l² – (m – n)² = (l)² – (m – n)² = [l + m – n] [l – (m – n)] = [l + m -n] [l – m + n]

Factorise the following:(i) x4 – y4(ii) a4 – (b + c)4(iii) l2 – (m – n)2

Answer»

(i) x⁴– y⁴

= (x²)² – (y²)² is in the form of a² – b²

a² – b² = (a + b) (a – b)

x⁴ – y⁴ = (x² + y²)(x² – y²)

= (x² + y²)(x + y)(x – y)

(ii) a⁴ – (b + c)⁴

a⁴ – (b + c)⁴

= (a²)² – [(b + c)²]²

= [a² + (b + c)²] [a² – (b + c)²] ,

= [a² + (b + c)²] (a + b + c) [a – (b + c)]

= [a² + (b + c)²] (a + b + c) (a – b – c)

(iii) l² – (m – n)²

l² – (m – n)²

= (l)² – (m – n)²

= [l + m – n] [l – (m – n)]

= [l + m -n] [l – m + n]