Practice questions for Factorization Class 8 Chapter 14

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Question 1
Factor the given expressions using identity:
(x+y)2= x2 +y2 +2xy
(x-y)2= x2 +y2 -2xy
x2 –y2 = (x-y) (x+y)
(i) p2 + 6p + 9
(ii) 4z2 – 4z + 1
(iii) 4p4 + 9p4 + 12p2q2
(iv) (a4 - 8a2b2 + 16b4) - 81
(v) 625 – x2 – 2xy – y2

Question 2
Divide as directed.
(i) 5(x + 1) (2x + 5) ÷ (2x + 5)
(ii) 39x(x + 5) (y - 2) ÷ 13x(y - 2)
(iii) 12pq (p + q) (q + r) (r + p) ÷ 6pq(q + r) (r + p)
(iv) 60(y - 4) (y2 + 5y + 3) ÷ 5(y - 4)
(v) x(x + 1) (x - 2) (x + 3) ÷ x(x - 2)

Question 3
Factorize the expressions.
(i) px² + qx
(ii) 7x² + 21y²
(iii) 2x³ + 2xy² + 2xz²
(iv) ap² + bq² + bp² + aq²
(v) nm + n2 + m + n
(vi) y (y - z) + 16 (y - z)
(vii) 5y² – 20y – 8z + 2yz
(viii) 10xy + 4x+ 5y + 2
(ix) 6xy - 4y + 6 - 9x

Question 4
Factor completely using the formula:
(i) 576 - p2 + 8pq - 16q2
(ii) 25x2 - (y + z)2
(iii) 4p2 - 4p - 3
(iv) 81 - x2- y2- 2xy
(v) 121 - x2- y2 - 2xy

Question 5
Factorize the expressions:
(i) 4a2- 12ab + 9b2
(ii) 36p2- 84pq + 49q2
(iii) 4a8- b8
(iv) (z - 1)2+ 2 (z-1) (2z+3) + (2z +3)2
(v) p2 -9q2