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1)12a²b³+3a³b²+16b²-a²
2)49c²-14c+1-21ac+3a
3)ax²+ay²+x^4+2x²y²+y^4
4)27c³-d³+9c²+3cd+d²
5)b³-2b²-2b+1

1)12a²b³+3a³b²+16b²-a²=3a²b²(4b+a) + (4²b² - a²)=3a²b²(4b+a)+(4b-a)(4b+a)=     = (4b+a)(3a²b² + 4b- a) 2) 49c² -14c+1 -21ac+3a =  (49c²-14c+1) -3a(7c - 1) = (7c - 1)²  - 3a(7c - 1) = =(7c-1)(7c - 1 - 3a) 3)ax²+ay²+x^4+2x²y²+y^4 = a(x²+y²)+(x^4+2x²y²+y^4) = a(x²+y²) +(x²+y²)²=   = (x²+y²) (a +x²+y²) 4)  27c³-d³+9c²+3cd+d² = [(3c)³-d³]+ (9c²+3cd+d²) = =[(3c - d)(9c²+3cd+d²)] + (9c²+3cd+d²) = (9c²+3cd+d²) (3c-d+1) 5) b³-2b²-2b+1 =(b³ + 1) - 2b( b+1) = (b+1)(b² -b+1) - 2b(b+1) =  = (b+1)(b² -b+1-2b) = (b+1)(b² -3b+1)