Factorise.
(i) 4 p2 - 9q2 (ii) 63a2 - 112b2 (iii) 49x2 - 36
(iv) 16x5 - 144x3 (v) (l + m)2 - (l - m)2 (vi) 9x2y2 - 16
(vii) (x2 - 2xy + y2) - z2 (viii) 25a2 - 4b2 + 28bc - 49c2
Solution:
(i) 4p2 - 9q2
= (2p)2 - (3q)2
= (2p + 3q) (2p - 3q) [Using identity a2 - b2 = (a - b)(a + b), considering a = 2p and b = 3q ]
(ii) 63a2 - 112b2
= 7(9a2 - 16b2 )
= 7 [(3a)2 - (4b)2]
= 7[(3a + 4b)(3a - 4b)] [Using identity x2 - y2 = (x - y)(x + y), considering x = 3a and y = 4b]
(iii) 49x2 - 36
= (7x)2 - (6)2
= (7x - 6)(7x + 6) [Using identity a2 - b2 = (a - b)(a + b), considering a = 7x and b = 6]
(iv) 16x5 - 144x3
= 16x3(x2 - 9)
= 16x3 [(x)2 - (3)2]
= 16x3 [(x - 3)(x + 3)] [Using identity a2 - b2 = (a - b)(a + b), considering a = x and b = 3]
(v) (l + m)2 - (l - m)2
= [(l + m) - (l - m)][(l + m) + (l - m)] [Using identity a2 - b2 = (a - b)(a + b), considering a= (l + m) and b = (l - m)]
= (l + m - l + m)(l + m + l - m)
= 2m × 2l
= 4ml
= 4lm
(vi) 9x2y2 - 16
= (3xy)2 - (4)2
= (3xy - 4)(3xy + 4) [Using the identity a2 - b2 = (a - b)(a + b), considering a = 3xy and b = 4]
(vii) (x2 - 2xy + y2 ) - z2
= (x - y)2 - (z)2 [Using identity (a - b)2 = a2 - 2ab + b2 for (x - y)2 = x2 - 2xy+ y2 ]
= (x - y - z)( x - y + z) [Using identity a2 - b2 = (a - b)(a + b), considering a = x - y and b = z.]
(viii) 25a2 - 4b2 + 28bc - 49c2
= 25a2 - (4b2 - 28bc + 49c2 )
= (5a)2 - [(2b)2 - 2 × 2b × 7c + (7c)2]
= (5a)2 - (2b - 7c)2 [Using identity (x - y)2 = x2 - 2xy + y2, considering x = 2b and y = 7c]
= [5a + (2b - 7c)][5a - (2b - 7c)] [Using identity x2 - y2 = (x - y)(x + y), considering x = 5a and y = 2b- 7c]
= (5a + 2b - 7c)(5a - 2b + 7c)
☛ Check: NCERT Solutions for Class 8 Maths Chapter 14
Video Solution:
Factorize (i) 4 p² - 9q² (ii) 63a² - 112b² (iii) 49x² - 36 (iv) 16x⁵ - 144x³ (v) (l + m)² - (l - m)² (vi) 9x²y² - 16 (vii) (x² - 2xy + y²) - z² (viii) 25a² - 4b² + 28bc - 49c²
Class 8 Maths NCERT Solutions Chapter 14 Exercise 14.2 Question 2
Summary:
Factorization of the following expressions (i) 4 p2 - 9q2 (ii) 63a2 - 112b2 (iii) 49x2 - 36 (iv) 16x5 - 144x3 (v) (l + m)2 - (l - m)2 (vi) 9x2y2 - 16 (vii) (x2 - 2xy + y2) - z2 (viii) 25a2 - 4b2 + 28bc - 49c2 are (i) (2p + 3q)(2p - 3q) (ii) 7[(3a + 4b)(3a - 4b)] (iii) (7x - 6)(7x + 6) (iv) 16x3 [(x - 3)(x + 3)] (v) 4lm (vi) (3xy - 4)(3xy + 4) (vii) (x - y - z)( x - y + z) (viii) (5a + 2b - 7c)(5a - 2b + 7c)
☛ Related Questions:
- 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.
- Factorise the expressions. (i) ax2 + bx (ii) 7p2 + 21q2 (iii) 2x3 + 2xy2 + 2xz2 (iv) am2 + bm2 + bn2 + an2 (v) (lm + l) + m + 1 (vi) y(y + z) + 9( y + z) (vii) 5y2 - 20 y - 8z + 2yz (viii) 10ab + 4a + 5b + 2 (ix) 6xy - 4 y + 6 - 9x.
- Factorise (i) a4 - b4 (ii) p4 - 81 (iii) x4 - ( y + z)4 (iv) x4 - (x - z)4 (v) a4 - 2a2b2 + b4
- Factorise the following expressions (i) p2 + 6 p + 8 (ii) q2 - 10q + 21 (iii) p2 + 6 p - 16
visual curriculum