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) x² + xy + 9x + 9y

(ii) 6xy - 4y + 6 – 9x

(iii) 10ab + 6a + 5b +3

(iv) x³ + x² + x + 1

(v) a² – y + ay – a

(vi) x³ – x²y + 5x - 5y



(vii) a(a + 3) – a – 3

(viii) 3ax + 3ay – 2bx – 2by

(ix) x(x + y – z ) – yz

(x) a³ – a² + ab² – a²b²



2. Factor grouping the algebraic expressions:

(i) 4xy – 7y + 12x – 21

(ii) 7ab – 5a – 28b + 20

(iii) 5xy – 2x – 5y² + 2y

(iv) 6x² – 15xz - 8yx + 20yz

(v) 4ax + 5bx – 12ay – 15by



3. Factorize by regrouping the terms:

(i) 7ab – 21bc – 7ax + 21xc

(ii) x² + xy(y + 1) + y³

(iii) ba² – 2a(1 - b) - 4

(iv) x² – 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) (x² + 2x)² – 7 (x² + 2x) – y (x² + 2x) +7y

(iv) a⁴x + a³ (2x – y ) – a(2ay + z) - 2z

(v) a³ – 2a²b + 3ab² – 6b³

(vi) a² + b – ab – a

(vii) 5xy – y² + 15zx - 3yz

(viii) ab² – bc² - ab + c²

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) (x² + 1) (x + 1)

(v) (a - 1) (a + y)

(vi) (x - y) (x² + 5)

(vii) (a + 3) (a - 1)

(viii) (x + y) (3a - 2b)

(ix) (x + y) (x – z)

(x) a(a - 1) (a – b²)

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 + y²) (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) (x² + 2x - 7) (x² + 2x - y)

(iv) (a + 2) (a³x – a²y - z)

(v) (a - 2) (a² + 3b²)

(vi) (a - 1) (a - b)

(vii) (y + 3z) (5x - y)

(viii) (ab – c²) (b – 1)

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