Worksheet on Factoring by Grouping

In worksheet on factoring by grouping we will solve different types of problems in factorization. In this sheet students can practice how to factor by grouping.

Factorization by grouping the following expressions:

1. Factor the following:

(i) 12x + 15

(ii) 14m - 21

(iii) 9n - 12n²

2. Factor by grouping the expressions:

(i) 16a² - 24ab

(ii) 15ab² - 20a²b

(iii) 12x² y³ - 21x³ y²

3. Factorize the expressions:

(i) 24x³ - 36x²y

(ii) 10x³ - 15x²

(iii) 36x³y - 60x²y³z

4. Factorize:

(i) 9x³ - 6x² + 12x

(ii) 8x² - 72xy + 12x

(iii) 18a³b³ - 27a²b³ + 36a³b²

5. How to factor by grouping?

(i) 14x³ + 21x⁴y - 28x²y²

(ii) -5 - 10t + 20t²

6. Factoring:

(i) x (x + 3) + 5(x + 3)

(ii) 5x (x - 4) - 7 (x - 4)                

(iii) 2m (1 - n) + 3(1 - n)

7. Factoring the expressions:

(i) 6a (a - 2b) + 5b (a - 2b)

(ii) x³ (2a - b) + x²(2a - b)

8. How to factor by grouping polynomials?

(i) 9a (3a - 5b) - 12a²(3a - 5b)

(ii) (x + 5)² - 4 (x + 5)

(iii) 3(a - 2b)² - 5(a - 2b)

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9. Factor completely:

(i) 2a + 6b - 3(a + 3b)²

(ii) 16(2p - 3q)² - 4(2p - 3q)

(iii) x (a - 3) + y (3 - a)

(iv) 12 (2x - 3y)² - 16 (3y - 2x)

(v) (x + y)(2x + 5) - (x + y)(x + 3)

10. How to factor by grouping polynomials?

(i) ar + br + at + bt

(ii) x² - ax - bx + ab

(iii) ab² - bc² - ab + c²

(iv) x² - xz + xy - yz

(v) 6ab - b² + 12ac - 2bc

11. Solve by factoring:

(i) (x - 2y)² + 4x - 8y

(ii) y² - xy (1 - x) - x³

(iii) (ax + by)² + (bx - ay)²

(iv) ab² + (a - 1)b - 1


12. Factoring Algebraic Expressions:

(i) x³ - 3x² + x - 3

(ii) ab (x² + y²) - xy (a² + b²)

(iii) x² - x(a + 2b) + 2ab

Answers for worksheet on factoring by grouping are given below to check the exact answer.

Answers:

1. (i) 3 (4x + 5)

(ii) 7 (2m - 3)

(iii) 3n (3 - 4n)


2. (i) 8a (2a - 3b)

(ii) 5ab (3b - 4a)

(iii) 3x²y²(4y - 7x)


3. (i) 12x²(2x - 3y)

(ii) 5x² (2x - 3)

(iii) 12x²y (3x - 5y²z)


4. (i) 3x (3x² - 2x + 4)

(ii) 4x (2x - 18y + 3)

(iii) 9a²b² (2ab - 3b + 4a)


5. (i) 7x² (2x + 3xy - 4y²)

(ii) -5 (1 + 2t - 4t²)


6. (i) (x + 3)(x + 5)

(ii) (x - 4)(5x - 7)

(iii) (1 - n)(2m + 3)


7. (i) (a - 2b)(6a + 5b)

(ii) x² (2a - b)(x + 1)


8. (i) 3a (3a - 5b)(3 - 4a)

(ii) (x + 5)(x + 1)

(iii) (a - 2b)(3a - 6b - 5)


9. (i) (a + 3b)(2 - 3a - 9b)

(ii) 4(2p - 3q)(8p - 12q - 1)

(iii) (a - 3)(x - y)

(iv) 4(2x - 3y)(6x - 9y + 4)

(v) (x + y)(x + 2)


10. (i) (r + t)(a + b)

(ii) (x - a)(x - b)

(iii) (b - 1)(ab - c²)

(iv) (x - z)(x + y)

(v) (b + 2c)(6a - b)


11. (i) (x - 2y)(x - 2y + 4)

(ii) (y - x)(y + x²)

(iii) (a² + b²)(x² + y²)

(iv) (b + 1)(ab - 1)


12. (i) (x² + 1)(x - 3)

(ii) (bx - ay)(ax - by)

(iii) (x - 2b)(x - a)

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