Using the following identity: (x + a)(x + b) = x^2 + (a + b)x + ab ⇒ 1003 × 999 = [1000 + (3)][ 000 + ( 1)] = 10002 + [(3) + ( 1)].1000 + (3)( 1) [Using the ...

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Standard VIII

Mathematics

Expansion of (x+a)(x+b)

1003 × 999=

Question

$1003 \times 999 =$ ___

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Solution

Using the following identity: $(x + a) (x + b) = x^{2} + (a + b) x + a b$
$\Rightarrow 1003 \times 999 = [1000 + (3)] [000 + (- 1)]$
$= 10002 + [(3) + (- 1)] .1000 + (3) (- 1) [U s i n g t h e i d e n t i t y (x + a) (x + b) = x 2 + (a + b) x + a b]$
$= 1000000 + (2) (1000) + (- 3)$
$= 1000000 + 2000 + (- 3)$
$= 1001997$
Therefore, the result is 1001997.

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1003×999= ___

Using the following identity: (x+a)(x+b)=x2+(a+b)x+ab ⇒1003×999=[1000+(3)][000+(−1)] =10002+[(3)+(−1)].1000+(3)(−1) [Using the identity (x+a)(x+b)=x2+(a+b)x+ab] =1000000+(2)(1000)+(−3) =1000000+2000+(−3) =1001997 Therefore, the result is 1001997.

$1003 \times 999 =$ ___