# Problems on Factorization of Expressions of the Form x$$^{2}$$ +(a + b)x +ab

Here we will solve different types of Problems on Factorization of Expressions of the Form x2 + (a + b)x + ab.

1. Factorize: a2 + 25a - 54

Solution:

Here, constant term = -54 = (27) × (-2), and 27 + (-2) = 25 (= coefficient of a).

Therefore, a2 + 25a – 54 = a2 + 27a - 2a - 54 (breaking 25a is sum of two terms, 27a - 2a)

= (a2 + 27a) + (- 2a - 54)

= a(a + 27) - 2(a + 27)

= (a + 27)(a  - 2).

2. Factorize: 3 - 4p + p2

Solution:

Here, constant term = 3 = (-3) × (-1), and (-3) + (-1) = -4 (= coefficient of p).

Therefore, 3 - 4p + p2 = p2 – 4p + 3

=p2 – 3p – p + 3 (breaking -4p is sum of two terms, -3p - p)

= (p2 – 3p) + (- p + 3)

= p(p - 3) - 1(p - 3)

= (p - 3)(p - 1).

3. Factorize: x2 – xy – 30y2

Solution:

Here, -30 = (-6) × 5,  and (-6) + 5 = -1 (= coefficient of xy).

Therefore, x2 – xy – 30y2 = x2 – 6xy + 5xy – 30y2 (breaking -xy is sum of two terms, -6xy + 5xy)

= (x2 – 6xy) + (5xy – 30y2)

= x(x – 6y) + 5y(x – 6y)

= (x – 6y)(x + 5y).

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