Question

Factorize the polynomials.

(y + 2) (y – 3) (y + 8) (y + 3) + 56

Answer 1

(y + 2) (y – 3) (y + 8) (y + 3) + 56 

= (y + 2)(y + 3)(y – 3)(y + 8) + 56 

= (y² + 3y + 2y + 6) (y² + 8y – 3y – 24) + 56 

= (y² + 5y + 6) (y² + 5y – 24) + 56 

= (m + 6) (m – 24) + 56 … [Putting y² + 5y = m]

= m (m – 24) + 6 (m – 24) + 56 

= m² – 24m + 6m – 144 + 56

 = m² – 18m – 88 

= m² – 22m + 4m – 88

 = m(m – 22) + 4(m – 22)

 = (m – 22) (m + 4) 

= (y² + 5y – 22)(y² + 5y + 4) … [Replacing m = y² + 5y] 

= (y² + 5y – 22) (y² + 4y + y + 4) 

= (y² + 5y – 22) [y(y + 4) + 1(y + 4)] 

= (y² + 5y – 22) (y + 4) (y + 1)