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Question
Use an expansion formula to find the values.
(i) (997)2 (ii) (102)2 (iii) (97)2 (iv) (1005)2
Use an expansion formula to find the values.
(i) (997)2 (ii) (102)2 (iii) (97)2 (iv) (1005)2
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Solution
It is known that, (a + b)2 = a2 + 2ab + b2 and (a − b)2 = a2 − 2ab + b2
(i) (997)2
= (1000 − 3)2
= (1000)2 − 2 × 1000 × 3 + (3)2
= 1000000 − 6000 + 9
= 994009
(ii) (102)2
= (100 + 2)2
= (100)2 + 2 × 100 × 2 + (2)2
= 10000 + 400 + 4
= 10404
(iii) (97)2
= (100 − 3)2
= (100)2 − 2 × 100 × 3 + (3)2
= 10000 − 600 + 9
= 9409
(iv) (1005)2
= (1000 + 5)2
= (1000)2 + 2 × 1000 × 5 + (5)2
= 1000000 + 10000 + 25
= 1010025
(i) (997)2
= (1000 − 3)2
= (1000)2 − 2 × 1000 × 3 + (3)2
= 1000000 − 6000 + 9
= 994009
(ii) (102)2
= (100 + 2)2
= (100)2 + 2 × 100 × 2 + (2)2
= 10000 + 400 + 4
= 10404
(iii) (97)2
= (100 − 3)2
= (100)2 − 2 × 100 × 3 + (3)2
= 10000 − 600 + 9
= 9409
(iv) (1005)2
= (1000 + 5)2
= (1000)2 + 2 × 1000 × 5 + (5)2
= 1000000 + 10000 + 25
= 1010025
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