Factorize the following polynomials.

(y+2) (y+3) (y-3) (y + 8) + 56

(y+2) (y+3) (y-3) (y + 8) + 56

⟹ (y² + 3y + 2y + 6) (y² + 8y - 3y - 24) + 5

⟹ (y² + 5y + 6) (y² + 5y - 24) + 56

Put (y² + 5y) = a

⟹ (a + 6) (a – 24) + 56

⟹ a² -24a + 6a – 144 + 56

⟹ a² – 18a – 88

⟹ a² -22a + 4a – 88

⟹ a (a-22) + 4 (a-22)

⟹ (a+4) (a-22)

⟹ But a = (y² + 5y)

⟹ ((y² + 5y) + 4) ((y² + 5y)-22)

⟹ (y² + 5y + 4) (y² + 5y -22)

⟹ (y² + 4y + y + 4) (y² + 5y -22)

⟹ (y (y+4) + 1(y+4)) (y² + 5y -22)

⟹ (y+1) (y+ 4) (y² + 5y -22)

Therefore, the factorized form = (y+1) (y+ 4) (y² + 5y -22)