Answer :

(i) 53 × 55

We can re–write 53 and 55 as


(50+3)× (50+5)


Using the identity


(x+a) (x+b) = x2 + (a+b) x + ab


(50+3)× (50+5) where x = 50, a = 3 and b = 5


= 502 + ( 3+5) 50 + 3× 5


=2500 + 400 + 15


= 2915


(ii) 102 × 106


= (100 + 2) (100 + 6)


Using the identity


(x+a) (x+b) = x2 + (a+b) x + ab


Here x= 100, a = 2 and b = 6


(100 + 2) (100 + 6)


= 1002 + ( 2+6) 100 + 2× 6


= 10000 + 800 +12


= 10812


(iii) 34 × 36


= (30+4) + (30+6)


Using the identity


(x+a) (x+b) = x2 + (a+b) x + ab


Here x = 30, a= 4 and b = 6


So, 302 +( 4+6) 30 +(4× 6)


= 900 + 300 +24


= 1224


(iv) 103 × 96


= (90 + 13) (90 +6)


Using the identity


(x+a) (x+b) = x2 + (a+b) x + ab


Here x = 90, a = 13 and b = 6


So, (90 + 13) (90 +6)


= 902 + ( 13+6) 90 +(13× 6)


= 8100 + 1710 +78


= 9888


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