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 a
^{2} – b
^{2} and factoring the quadratic trinomials.
1. Factorize each of the following expression.
(i) – 5x
^{2} + 5xy – 52x
(ii) p
^{2}qr + pq
^{2}r + pqr
^{2}
(iii) – 4p
^{5} – 16p
^{3}q – 20p
^{2}q
^{2}
(iv) p
^{3}qr + 4pq
^{3} + 14p
^{3}
(v) – x
^{2} + 3x + x – a - 2
(vi) a
^{2}m + b
^{2}m + c
^{2}m - a
^{2}n - b
^{2}n - c
^{2}n
2. Factorize using the formula of difference of two squares:
(i) 25x
^{2} – 36x
^{2}y
^{2}
(ii) 49m
^{2} – n
^{4}
(iii) 81a
^{4} – b
^{2}
(iv) x
^{3} – 25x
(v) 32a
^{2}b – 200b
^{3}
(vi) 4a
^{2} + 12ab + 9b
^{2} - 9
3. Find the values of:
(i) (64)
^{2} – (36)
^{2}
(ii) (8
^{2}/
_{3})
^{2} – (3
^{1}/
_{3})
^{2}
(iii) (42)
^{2} – (28)
^{2}
(iv) (10003)
^{2} – (9997)
^{2}
(v) (9.2)
^{2} – (0.8)
^{2}
4. Factorization of trinomial:
(i) 10p
^{2}q
^{2} – 11pq + 3
(ii) 12x
^{2} + 11x – 5
(iii) 15a
^{2}b
^{2} – 21ab + 6
(iv) 9x
^{2} – y
^{2} - 8y – 16
(v) x
^{4} – 10x
^{2} + 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) - 4p
^{2}(p
^{3} + 4pq + 5q
^{2})
(iv) p(p
^{2}qr + 4q
^{3} + 14p
^{2})
(v) (a – 1) (a – x + 2)
(vi) (m – n) (a
^{2} + b
^{2} + c
^{2})
2. (i) x
^{2}(5 + 6y) (5 – 6y)
(ii) (7m + n
^{2}) (7m - n
^{2})
(iii) (9a
^{2} + b) (9a
^{2} - 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)
`
8th Grade Math Practice
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