Verified answer

1)

x²y+x+xy²+y+2xy+2  = (x²y+xy²+2xy)+(х+у+2) =

= ху(х+у+2) +(х+у+2) = (х+у+2)·(ху+1)

2)

9a²-16  = (3а)² - 4² = (3а- 4)·(3а+4)

3)

x²-8ax+16a²  = x²- 2 ·х · 4а + (4a)²  = (х - 4а)² = (х - 4а)·(х - 4а)

4)

(a+2b)²-(3a-b)²  = ((a+2b)-(3a-b))  · ((a+2b) + (3a-b)) =

= (a+2b-3a+b)  · (a+2b + 3a-b) = (- 2a +3b)·(4a+b)

5)

x²+2xy+y²-a² = (x²+2xy+y²) - a² = (x+y)² - a² = (x+y-a)·(x+y+a)