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Worksheet on Factorization



Practice the worksheet on factorization. The questions are based on factoring the expressions, factoring the difference of two squares, evaluating the expression using the formula a2 – b2 and factoring the quadratic trinomials.

1. Factorize each of the following expression.

(i) – 5x2 + 5xy – 52x

(ii) p2qr + pq2r + pqr2

(iii) – 4p5 – 16p3q – 20p2q2

(iv) p3qr + 4pq3 + 14p3

(v) – x2 + 3x + x – a - 2

(vi) a2m + b2m + c2m - a2n - b2n - c2n



2. Factorize using the formula of difference of two squares:

(i) 25x2 – 36x2y2

(ii) 49m2 – n4

(iii) 81a4 – b2

(iv) x3 – 25x

(v) 32a2b – 200b3

(vi) 4a2 + 12ab + 9b2 - 9



3. Find the values of:

(i) (64)2 – (36)2

(ii) (82/3)2 – (31/3)2

(iii) (42)2 – (28)2

(iv) (10003)2 – (9997)2

(v) (9.2)2 – (0.8)2



4. Factorization of trinomial:

(i) 10p2q2 – 11pq + 3

(ii) 12x2 + 11x – 5

(iii) 15a2b2 – 21ab + 6

(iv) 9x2 – y2 - 8y – 16

(v) x4 – 10x2 + 9


Answers for the worksheet on factorization are given below to check the exact answers of the above set of factorization.


Answers:


1. (i) x(- 5x + 5y – 52)                     

(ii) pqr(p + q + r)

(iii) - 4p2(p3 + 4pq + 5q2)

(iv) p(p2qr + 4q3 + 14p2)

(v) (a – 1) (a – x + 2)

(vi) (m – n) (a2 + b2 + c2)



2. (i) x2(5 + 6y) (5 – 6y)

(ii) (7m + n2) (7m - n2)

(iii) (9a2 + b) (9a2 - b)

(iv) x(x + 5) (x – 5)

(v) 2b(4a + 10b) (4a – 10b)

(vi) (2a + 3b + 3) (2a + 3b – 3)


3. (i) 2800

(ii) 64

(iii) 980

(iv) 120000

(v) 84


4. (i) (2pq – 1) (5pq – 3)

(ii) (3x – 1) (4x + 5)

(iii) 3(ab – 1) (5ab – 2)

(iv) (3x + y + 4) (3x – y – 4)

(v) (x + 1) (x – 1) (x + 3) (x – 3)






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