Question

evaluate using suitable identity (999)

$999 {}^{2} - 1$
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Answer 1

ANSWER

(999)² - 1 = 998000

EXPLANATION

The given number is : (999)² - 1

1 is same as 1²

⟹ (999)² - (1)²

By using identity: a² - b² = ( a + b)( a - b )

Here, a corresponds with 999 and b corresponds with 1

⟹ ( 999 + 1 )( 999 - 1 )

⟹ ( 1000 )( 998 )

⟹ 998000

998000 is the answer

MORE

An identity refers to an equality that is true for any value in it.

a² - b² = ( a + b)( a - b ) is one of the standard algebraic identity.

We can obtain this identity:

( a + b )( a - b )

⟹ a( a - b ) + b( a + b )

⟹ a² - ab + ba + b²

ab is same as ba, which when simplified, gives us:

⟹ a² - b²

hence, a² - b² = ( a + b)( a - b )