Worksheet on Factorization by Regrouping
Practice the worksheet on factorization by regrouping the
terms. We know, we need to arrange the given algebraic expression in such a
way, that a common factor can be taken out from each group.
1. Factorize each of the following by regrouping:
(i) x
^{2} + xy + 9x + 9y
(ii) 6xy  4y + 6 – 9x
(iii) 10ab + 6a + 5b +3
(iv) x
^{3} + x
^{2} + x + 1
(v) a
^{2} – y + ay – a
(vi) x
^{3} – x
^{2}y + 5x  5y
(vii) a(a + 3) – a – 3
(viii) 3ax + 3ay – 2bx – 2by
(ix) x(x + y – z ) – yz
(x) a
^{3} – a
^{2} + ab
^{2} – a
^{2}b
^{2}
2. Factor grouping the algebraic expressions:
(i) 4xy – 7y + 12x – 21
(ii) 7ab – 5a – 28b + 20
(iii) 5xy – 2x – 5y
^{2} + 2y
(iv) 6x
^{2} – 15xz  8yx + 20yz
(v) 4ax + 5bx – 12ay – 15by
3. Factorize by regrouping the terms:
(i) 7ab – 21bc – 7ax + 21xc
(ii) x
^{2} + xy(y + 1) + y
^{3}
(iii) ba
^{2} – 2a(1  b)  4
(iv) x
^{2} – x(a + 4b) + 4ab
(v) x – 9  (x – 9)
^{2} + xy – 9y
4. Factorize by grouping the following expressions:
(i) (p  4) – (p – 4)
^{2} + 12 – 3p
(ii) q (r – s )
^{2} – p (s  r) + 3r – 3s
(iii) (x
^{2} + 2x)
^{2} – 7 (x
^{2} + 2x) – y (x
^{2} + 2x) +7y
(iv) a
^{4}x + a
^{3} (2x – y ) – a(2ay + z)  2z
(v) a
^{3} – 2a
^{2}b + 3ab
^{2} – 6b
^{3}
(vi) a
^{2} + b – ab – a
(vii) 5xy – y
^{2} + 15zx  3yz
(viii) ab
^{2} – bc
^{2}  ab + c
^{2}
Answers for the worksheet on
factorization by regrouping the terms are given below to check the exact answers
of the above factors.
Answers:
1. (i) (x + y) (x
+ 9)
(ii) (2y  3) (3x  2)
(iii) (2a + 1) (5b + 3)
(iv) (x
^{2} + 1) (x + 1)
(v) (a  1) (a + y)
(vi) (x  y) (x
^{2} + 5)
(vii) (a + 3) (a  1)
(viii) (x + y) (3a  2b)
(ix) (x + y) (x – z)
(x) a(a  1) (a – b
^{2})
2. (i) (y + 3) (4x  7)
(ii) (a  4) (7b  5)
(iii) (x  y) (5y  2)
(iv) (3x  4y) (2x  5z)
(v) (x – 3y) (4a + 5b)
3. (i) 7(b  x) (a – 3c)
(ii) (x + y
^{2}) (x + y)
(iii) (a + 2) (ab – 2)
(iv) (x – 4b) (x  a)
(v) (x  9) (10 – x + y)
4. (i) (p – 4) (2 – p)
(ii) (r – s) (qr – qs + p + 3)
(iii) (x
^{2} + 2x  7) (x
^{2} + 2x  y)
(iv) (a + 2) (a
^{3}x – a
^{2}y  z)
(v) (a  2) (a
^{2} + 3b
^{2})
(vi) (a  1) (a  b)
(vii) (y + 3z) (5x  y)
(viii) (ab – c
^{2}) (b – 1)
8th Grade Math Practice
Math Homework Sheets
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