Factorise

(i)


(ii)


(iii)


(iv)


(v) (l + m)2 - (l - m)2


(vi)


(vii)


(viii)

(i) 4p2 - 9q2


4p2 - 9q2 = (2p)2 - (3q)2


Using identity a2 - b2 = (a + b)(a - b)


Here a = 2p; b = 3q


(2p)2 - (3q)2 = (2p + 3q) (2p – 3q)



(ii) 63a2 - 112b2


7(9a2 - 16b2) = 7{(3a)2 - (4b2)}


Using identity a2 - b2 = (a + b)(a - b)


Here a = 3a; b = 4b


7{(3a)2 - (4b)2} = 7{(3a + 4b) (3a – 4b)}



(iii) 49x2 - 36 = (7x)2 - 62


Using identity a2 - b2 = (a + b)(a - b)


Here a = 7x; b = 6


(7x)2 - (6)2 = (7x + 6) (7x – 6)


 


(iv) 16x⁵ - 144x3 = 16x3(x2 - 9) ⇒ 16x3{x2 - 32}


Using identity a2 - b2 = (a + b)(a - b)


Here a = x; b = 3


16x3{(x)2 - (3)2} = 16x3{(x + 3) (x – 3)}



(v) (l + m)2 - (l - m)2


Using identity a2 - b2 = (a + b)(a - b)


Here a = (l + m); b = (l - m)


(l + m)2 - (l + m)2 = (l + m + l - m) (l + m – l + m)


⇒ (l + m)2 - (l + m)2 = 2l × 2m = 4lm




(vi) 9x2y2 - 16 = (3xy)2 - 42


Using identity a2 - b2 = (a + b)(a - b)


Here a = 3xy; b = 4


(3xy)2 - 42 = (3xy + 4) + (3xy - 4)




(vii) (x2- 2xy + y2 ) = (x + y)2 [using identity (a + b)2 = a2 + 2ab + b2]


(x + y)2 - z2 =


Using identity a2 - b2 = (a + b)(a - b)


Here a = (x + y)2 ; b = z


(x + y)2 - z2 = (x + y + z) + (x + y - z)




(viii) 25a2 - (4b2 - 28bc + 49c2) ⇒ (5a)2 - (2b – 7c )2 [using identity (a - b)2 = a2 - 2ab + b2]


Using identity a2 - b2 = (a + b)(a - b)


Here a = 5a ; b = 4b – 7c


(5a)2 - (2b – 7c )2 = (5a + 2b – 7c) + (5a – 2b + 7c)


 

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