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)

9th Grade Math

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