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  12n
^{2}
2. Factor by grouping the expressions:
(i) 16a
^{2}  24ab
(ii) 15ab
^{2}  20a
^{2}b
(iii) 12x
^{2} y
^{3}  21x
^{3} y
^{2}
3. Factorize the expressions:
(i) 24x
^{3}  36x
^{2}y
(ii) 10x
^{3}  15x
^{2}
(iii) 36x
^{3}y  60x
^{2}y
^{3}z
4. Factorize:
(i) 9x
^{3}  6x
^{2} + 12x
(ii) 8x
^{2}  72xy + 12x
(iii) 18a
^{3}b
^{3}  27a
^{2}b
^{3} + 36a
^{3}b
^{2}
5. How to factor by grouping?
(i) 14x
^{3} + 21x
^{4}y  28x
^{2}y
^{2}
(ii) 5  10t + 20t
^{2}
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) x
^{3} (2a  b) + x
^{2}(2a  b)
8. How to factor by grouping polynomials?
(i) 9a (3a  5b)  12a
^{2}(3a  5b)
(ii) (x + 5)
^{2}  4 (x + 5)
(iii) 3(a  2b)
^{2}  5(a  2b)
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) x
^{2}  ax  bx + ab
(iii) ab
^{2}  bc
^{2}  ab + c
^{2}
(iv) x
^{2}  xz + xy  yz
(v) 6ab  b
^{2} + 12ac  2bc
11. Solve by factoring:
(i) (x  2y)
^{2} + 4x  8y
(ii) y
^{2}  xy (1  x)  x
^{3}
(iii) (ax + by)
^{2} + (bx  ay)
^{2}
(iv) ab
^{2} + (a  1)b  1
12. Factoring Algebraic Expressions:
(i) x
^{3}  3x
^{2} + x  3
(ii) ab (x
^{2} + y
^{2})  xy (a
^{2} + b
^{2})
(iii) x
^{2}  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) 3x
^{2}y
^{2}(4y  7x)
3. (i) 12x
^{2}(2x  3y)
(ii) 5x
^{2} (2x  3)
(iii) 12x
^{2}y (3x  5y
^{2}z)
4. (i) 3x (3x
^{2}  2x + 4)
(ii) 4x (2x  18y + 3)
(iii) 9a
^{2}b
^{2} (2ab  3b + 4a)
5. (i) 7x
^{2} (2x + 3xy  4y
^{2})
(ii) 5 (1 + 2t  4t
^{2})
6. (i) (x + 3)(x + 5)
(ii) (x  4)(5x  7)
(iii) (1  n)(2m + 3)
7. (i) (a  2b)(6a + 5b)
(ii) x
^{2} (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  c
^{2})
(iv) (x  z)(x + y)
(v) (b + 2c)(6a  b)
11. (i) (x  2y)(x  2y + 4)
(ii) (y  x)(y + x
^{2})
(iii) (a
^{2} + b
^{2})(x
^{2} + y
^{2})
(iv) (b + 1)(ab  1)
12. (i) (x
^{2} + 1)(x  3)
(ii) (bx  ay)(ax  by)
(iii) (x  2b)(x  a)
8th Grade Math Practice
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