1) а⁴+а³+а+1=

2) m⁶-m⁴+2m³+2m²=

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).