Factorize the following expressions.
(i) a2 + 8a +16 (ii) p2 - 10 p + 25 (iii) 25m2 + 30m + 9
(iv) 49 y2 + 84 yz + 36z2 (v) 4x2 - 8x + 4
(vi) 121b2 - 88bc +16c2 (vii) (l +m)2 - 4lm (Hint: Expand (l + m)2 first)
(viii) a4+ 2a2b2 + b4
Solution:
(i) a2 + 8a +16
= (a)2 + 2 × a × 4 + (4)2
= (a + 4)2 [Using identity (x + y)2 = x2 + 2xy + y2, considering x = a and y = 4 ]
(ii) p2 - 10 p + 25
= (p)2 - 2 × p × 5 + (5)2
= (p - 5)2 [Using identity (a - b)2 = a2 - 2ab + b2, considering a = p and b = 5 ]
(iii) 25m2 + 30m + 9
= (5m)2 + 2 × 5m × 3 + (3)2
= (5m + 3)2 [Using identity (a + b)2 = a2 + 2ab + b2, considering a = 5m and b = 3 ]
(iv) 49y2 + 84yz + 36z2
= (7y)2 + 2 × (7y) × (6z) + (6z)2
= (7y + 6z)2 [Using identity (a + b)2 = a2 + 2ab + b2, considering a = 7y and b = 6z]
(v) 4x2 - 8x+ 4
= (2x)2 - 2(2x)(2) + (2)2
= (2x - 2)2 [Using identity (a - b)2 = a2 - 2ab + b2, considering a = 2x and b = 2]
= [(2)(x -1)]2 = 4(x -1)2
(vi) 121b2 - 88bc+16c2
= (11b)2 - 2(11b)(4c) + (4c)2
= (11b - 4c)2 [Using identity (a - b)2 = a2 - 2ab + b2, considering a = 11b and b = 4c]
(vii) (l + m)2 - 4lm
= l2 + 2lm+ m2 - 4lm [Using identity (a + b)2 = a2 + 2ab + b2]
= l2 - 2lm + m2
= (l - m)2 [Using identity (a - b)2 = a2 - 2ab + b2, considering a = l and b = m]
(viii) a4 + 2a2b2 + b4
= (a2)2 + 2 (a2)(b2) + (b2)2
= (a2 + b2)2 [Using identity (x + y)2 = x2 + 2xy + y2, considering x = a2 and y = b2]
☛ Check: NCERT Solutions for Class 8 Maths Chapter 14
Video Solution:
Factorize the following expressions. (i) a² + 8a +16 (ii) p² -10 p + 25 (iii) 25m² + 30m + 9 (iv) 49 y² + 84 yz + 36z² (v) 4x² - 8x + 4 (vi) 121b² - 88bc +16c² (vii) (l +m)² - 4lm (Hint: Expand (l + m)² first) (viii) a⁴+ 2a²b² + b⁴
Class 8 Maths NCERT Solutions Chapter 14 Exercise 14.2 Question 1
Summary:
The following expressions (i) a2 + 8a +16 (ii) p2 -10 p + 25 (iii) 25m2 + 30m + 9 (iv) 49 y2 + 84 yz + 36z2 (v) 4x2 - 8x + 4 (vi) 121b2 - 88bc +16c2 (vii) (l +m)2 - 4lm (viii) a4+ 2a2b2 + b4 are factorised as (i) (a + 4)2 (ii) (p- 5)2 (iii) (5m + 3)2 (iv) (7y + 6z)2 (v) 4(x -1)2 (vi) (11b - 4c)2 (vii) (l - m)2 (viii) (a2 + b2)2
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