Find the value of the given expression using multiplication idendities. $24 \times 76 + 105 \times 209$

23763

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23765

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23769

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23761

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Solution

The correct option is C
23769

The given expression is

$24 \times 76 + 105 \times 209$

$= (20 + 4) (80 - 4) + (100 + 5) (200 + 9)$

$= (20 \times 80 + 4 \times 80 - 20 \times 4 - 4 \times 4) + (100 \times 200 + 100 \times 9 + 5 \times 200 + 5 \times 9$ )

$= (1600 + 320 - 80 - 16) + (20000 + 900 + 1000 + 45)$

$= 23769$

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