Question
Evaluate the product without multiplying directly: $103 \times 107$
✓
Answer
$103 \times 107$
$103\times 107$ can also be written as$(100+3)(100+7).$
We can observe that we can apply the identity $(x+a)(x+b)$
$=x^2 + (a+b)x + ab$
$(100+3)(100+7)$
$=(100)^2 + (3 + 7)(100) + 3\times 7$
$=10000 + 1000 + 21$
$= 11021$
Therefore, we conclude that the value of the product $103 \times 107$ is $11021.$
$103\times 107$ can also be written as$(100+3)(100+7).$
We can observe that we can apply the identity $(x+a)(x+b)$
$=x^2 + (a+b)x + ab$
$(100+3)(100+7)$
$=(100)^2 + (3 + 7)(100) + 3\times 7$
$=10000 + 1000 + 21$
$= 11021$
Therefore, we conclude that the value of the product $103 \times 107$ is $11021.$
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