Problems on Factorization by Grouping of Terms

Here we will solve different types of Problems on Factorization by grouping of terms.

1. Factorize: a2 – (b – 5)a – 5b.

Solution:

Given expression = a2 – (b – 5)a – 5b

= a2 – ba + 5a – 5b

= a(a - b) + 5(a - b)

= (a – b)(a + 5).

2. Factorize: a2 + b2 + a + b + 2ab

Solution:

Given expression = a2 + b2 + a + b + 2ab

= a2 + 2ab + b2 + (a + b)

= (a + b)2 + (a + b)

= (a + b){(a + b) + 1}

= (a + b)(a + b + 1).

3. Find the factors by grouping of terms: x2 – 2x – 2y + xy

Solution:

Given expression = x2 – 2x – 2y + xy

= x2 – 2x + xy – 2y

= x(x – 2) + y(x – 2)

= (x – 2)(x + y).

Therefore, the factors are x – 2 and x + y.

4. Factorize: 5x3 – 15x2 – x + 3

Solution:

Given expression = 5x3 – 15x2 – x + 3

= 5x2(x – 3) – 1(x – 3)

= (x – 3)(5x2 – 1)

5. Factorize by grouping: x2 – (a + 4)x + 4a

Solution:

Given expression = x2 – (a + 4)x + 4a

= x2 – ax – 4ax + 4a

= x(x – a) – 4a(x – a)

= (x – a)(x – 4a)

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