3. Using some algebraic identity , evaluate the following 
(a) (1007)2
(b) (93)2
(c) 996*1004
(d) 503*495

Dear Student,

a 10072 = 1000+72Using Identity: a+b2 = a2+b2+2ab= 10002+72+2×1000×7= 1000000+49+14000= 1014049b 932 = 100-72Using Identity: a-b2 = a2+b2-2ab= 1002+72-2×100×7= 10000+49-1400= 8649c 996×1004= 1000-41000+4Using Identity x+yx-y = x2-y2where x= 1000, y =4= 10002-42= 1000000-16= 999984d 503×495Using Identity: x+ax+b = x2+a+bx+abwhere x = 500, a= 3, b=-5= 5002+3-5500+3×-5= 250000+-2500-15= 250000-1000-15= 248985
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