Question

simplify a^4-(a-b)^4

Answer 1

a^4-(a^4-b^4)
a^4-(a^2+b^2)(a^2-b^2)
a^4-(a^2+b^2)(a+b)(a-b)

Answer 2

a⁴-(a-b)⁴

= a⁴-(a⁴-4a³b-6a²b²-4ab³+b⁴) (using Pascale triangle)

= a⁴-a⁴+4a³b+6a²b²+4ab³-b⁴

= 4a³b+6a²b²+4ab³-b⁴

or

a⁴-(a-b)⁴

= (a²)²-((a-b)²)²

= (a²+(a-b)²) (a²-(a-b²)

= (a²+(a²-2ab+b²) ((a+(a-b) (a-(a-b))

= (a²+a²-2ab+b²)(a+a-b)(a-a+b)

= (2a²-2ab+b²)(2a-b)(b)