Разложите на множители а) х⁵-х³у²-х²у³+у⁵ б)m⁵+m³n²+m²n³+n⁵ в)а⁵-4а³-8а²+32 г)27-27р²+р³-р⁵ д)х⁶+2х³у³+у⁶ е)а⁵b-a³b³-a²b⁴+b⁶

а) х⁵-х³у²-х²у³+у⁵=x³(x²-y²)-y³(x²-y²)=(x²-y²)(x³-y³)=(x-y)(x+y)(x-y)(x²+xy+y²)

б)m⁵+m³n²+m²n³+n⁵=m³(m²+n²)+n³(m²+n²)=(m²+n²)(m³+n³)=(m²+n²)(m+n)(m²-mn+n²)

в)а⁵-4а³-8а²+32=a³(a²-4)-8(a²-4)=(a²-4)(a³-8)=(a-2)(a+2)(a-2)(a²+2a+4)

г)27-27р²+р³-р⁵=27(1-p²)+p³(1-p²)=(1-p²)(27+p³)=(1-p)(1+p)(3+p)(9-3p+p²)

д)х⁶+2х³у³+у⁶=(x³+y³)²=(x+y)²(x²-xy+y²)²=(x+y)(x+y)(x²-xy+y²)(x²-xy+y²)

е)а⁵b-a³b³-a²b⁴+b⁶=a³b(a²-b²)-b⁴(a²-b²)=(a²-b²)(a³b-b⁴)=b(a-b)(a+b)(a³-b³)=

=b(a-b)(a+b)(a-b)(a²+ab+b²)