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3b+bc+3ac+9a

a^2y^2-x^6

c^2-6c+9-4x^2

xy^2+y+x^2y+x+4xy+4

3b+bc+3ac+9a = (3b+bc) + (3ac+9a) = b (3+c) + 3a (c+3) = (c+3) (b+3a)

a²y²-x⁶ = (ay) ² - (x³) ² = (ay-x²) (ay+x²)

c²-6c+9-4x² = (c²-6c+9) - 4x² = (c-3) ² - (2x) ² = (c-3-2x) (c-3+2x)

xy²+y+x²y+x+4xy+4 = (xy²+y) + (x²y+x) + (4xy+4) = y (xy+1) + x (xy+1) + 4 (xy+1) =

= (xy+1) (y+x+4)