Factorize the polynomials.(y + 2) (y – 3) (y + 8) (y + 3) + 56

1.	Factorize the polynomials.(y + 2) (y – 3) (y + 8) (y + 3) + 56
Answer» (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)

Answer»

(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)

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