Question

x^4 - (x-y)^4
Factories​

Answer 1

x⁴ - (x-y)⁴

(x²)² - [(x-y)²]²

Using identity : a²-b² = (a+b)(a-b)

[x²+(x-y)²][(x²-(x-y)²]

Some more identities :

(a+b)² = a² + 2ab + b²

(a-b)² = a² - 2ab + b²

(x+a)(x+b) = x² + x(a+b) + (ab)

(a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca

(a+b)³ = a³ + 3a²b + 3ab² + b³

a³+b³ = (a+b)(a²-ab+b²)

(a-b)³ = a³ - 3a²b + 3ab² - b³

a³-b³ = (a-b)(a²+ab+b²)

a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)

Conditional identity:

if a+b+c = 0

a³+b³+c³ = 3abc