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

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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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