8. Factorise each of tM follo 1oing: (i} &3 + b3 + 1242b + 6ab2 (i'i) 843 -.b3 - 12a2b + 6ab2 (iii) 27. - 126a3 - 135a + 22&rZ (iv) 64a3 -27b3 - J44a2b + 108ab2 1 (v) 27p3 - - - - !!.p2 + !._p 216 2 4 .

Ci) 8a3 + b8 + 12.a2b + 6ab2 = (2a)3 + (b>3 + S(2a)(bX2a + b) = (2a + bi3 [Using identity: x3 + y3 + aty(x + y) = + y)3] = (2a + b)(2a + b)(2a + b). (i) aaa -ba - 12a2b + 6ab2 = (2a>3 -(b'/3 - 3(2a)2b + 3(2a>b2 = (2a - b'f [Using identity: x3 - y8 - :U2y + 3%y2 = ex - y)3] = (2a - b)(2a - b)(2a - b). (iii') 27 - 125a8 - l36a + 225a2 = (3)3 - C6a>3 - 3 x C3>2 x (6a)+ 3(3X5a>2 "" (3 - 5a>3 [Using identity: x3 - y8 - 3% + 3%y2 = ex - y )8] "" (3 - 6a)(3 - fla)(3 - 5a). (iv) 64a3 - 27b3 - 144a2b + 108ab2 = (4a)3 - (3bl3 - 3(4af(3b) + 3(4a)(3b>2 = (4a - 3b)3 [Using identity: r.3 -y8 - 3% + azy2 = (.r _ y)3] = (4a '."" 3bX4a - 3b)(4a - 3b). (v) 27pa - _1_ - p2 + != (3p"I - ( a- 3 x (3p)2 IB 2 4 6 . )( + 3 )( (3p) x (J 42 = (Sp-)8 [Using identity: -:i -3% + 3x.>'2 = (% - Y)8]