The Total solution for NCERT class 6-12
We know that a3 + b3 = (a + bf –3ab(a + b) and a3 – b3 = (a – bf + 3 ab(a – b)(i) 1113 – 893= (111 – 89)3 + 3 x ill x 89(111 – 89)= (22)3 + 3 x 111 x 89 x 22= 10648 + 652014 = 662662(OR)(a + b)3 – (a – b)3 = 2(b3 + 3a2b)= 1113 – 893 = (100 + 11)3 –(100 – 11)3= 2(113 + 3 x 1002 x 11]= 2(1331 + 330000]= 331331 x 2 = 662662(a + b)3 + (a- b)3 = 2(b3 + 3ab2)(ii) 463 + 343 = (40 + 6)3 +(40 – 6)3= 2[(40)3 + 3 x 40 x 62]= 2[64000 + 3 x 40 x 36]= 2[64000 + 4320]= 2 x 68320 = 136640(iii) 1043 + 963 = (100 + 4)3 +(100 – 96)3= 2 [a3 + 3 ab2]= 2[(100)3 + 3 x 100 x (4)2]= 2[ 1000000 + 300 x 16]= 2[ 1000000 + 4800]= 1004800 x 2 = 2009600(iv) 933 – 1073 = -[(107)3 –(93)3]= -[(100 + If – (100 – 7)3]= -2[b3 + 3a2b)]= -2[(7)3 + 3(100)2 x 7]= -2(343 + 3 x 10000 x 7]= -2[343 + 210000]= -2[210343] = -420686