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1) a⁴+a⁴+a+1=a³(a+1)+a+1=(a+1)(a³+1)=(a+1)(a+1)(a²-a+1)=(a+1)²(a²-a+1).
2) m⁶-m⁴+2m³+2m²= m⁴(m²-1)+2m²(m+1)=m⁴(m+1)(m-1)+2m²(m+1)=
=(m+1)(m⁴(m-1)+2m²)=(m+1)m²(m²(m-1)+2=m²(m+1)(m³-m²+2)=
=m²(m+1)(m³+m²-m²-m²+2)=m²(m+1)(m³+m²-2m²+2)=m²(m+1)(m²(m+1)-2(m²-1))=
=m²(m+1)(m²(m+1)-2(m+1)(m-1)=m²(m+1)(m+1)(m²-2(m-1))=m²(m+1)²(m²-2m+2).
2) m⁶-m⁴+2m³+2m²= m⁴(m²-1)+2m²(m+1)=m⁴(m+1)(m-1)+2m²(m+1)=
=(m+1)(m⁴(m-1)+2m²)=(m+1)m²(m²(m-1)+2=m²(m+1)(m³-m²+2)=
=m²(m+1)(m³+m²-m²-m²+2)=m²(m+1)(m³+m²-2m²+2)=m²(m+1)(m²(m+1)-2(m²-1))=
=m²(m+1)(m²(m+1)-2(m+1)(m-1)=m²(m+1)(m+1)(m²-2(m-1))=m²(m+1)²(m²-2m+2).
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