413
1) 3a²+10a+3=3(a+3)(a+1/3)
3a²+10a+3=3(a²+3a+1/3a+1)
3a²+10a+3= 3a²+9a+a+3
3a²+10a+3= 3a²+10a+3 доказано
2)
(a+1)(a²+5a+6)=(a²+3a+2)(a+3)
a³+a²+5a²+6a+6=a³+3a²+2a+3a²+9a+6
a³+6a²+11a+6=a³+6a²+11a+6 доказано
3)
(a+1)(a⁴-a³+a²-a+1)=a⁵+1
a⁵+a⁴-a⁴-a³+a³+a²-a²-a+a+1=a⁵+1
a⁵+1=a⁵+1 доказано
415
(n+29)(n+3)-(n+7)(n+1)=8
n²+29n+3n+87- (n²+7n+n+7)=8
n²+32n+87-n²-8n-7=8
24n+80=8
24n=8-80
24n= - 72
n= -3