Evaluate 1002 × 998 by using a special product.
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We can write 1002 × 998 as (1000 + 2)(1000 - 2).
As (a - b)(a + b) = (a2 - b2)
We get,
(1000 + 2)(1000 - 2) = 10002 - 22 = 1000000 - 4 = 999996.
Hence, 1002 × 998 = 999996.
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Find the expansions of the following :
(i) (2x + 3y + 5)(2x + 3y - 5)
(ii) (6 - 4a - 7b)2
(iii) (7 - 3xy)3
(iv) (x + y + 2)3
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If 2x = 3y - 5, then find the value of 8x3 - 27y3 - 90xy + 125.