Question

Factorise:x^4-(x-y)^4​

Answer 1

Answer:

x⁴ - (x-y)⁴ = [ x+ (x-y)]² [ x -(x-y)]²

...........[ since, (a+b)(a-b) = a²-b²]

= ( x+x-y )² ( x-x+y)²

= (2x-y)² (y)²

= (2x)² -2(2x)(y) + y² (y²)

= y²[ 4x²- 4xy +y²]

= 4x²y² - 4xy³ +y⁴

Answer 2

Answer:

x⁴ - (x-y)⁴ = [ x+ (x-y)]² [ x -(x-y)]²

...........[ since, (a+b)(a-b) = a²-b²]

= ( x+x-y )² ( x-x+y)²

= (2x-y)² (y)²

= (2x)² -2(2x)(y) + y² (y²)

= y²[ 4x²- 4xy +y²]

= 4x²y² - 4xy³ +y⁴