Question
Evaluate the product without multiplying directly: $95 \times 96$
✓
Answer
$95 \times 96$
$95 \times 96{\text{ can also be written as}}\left( {100 - 5} \right)\left( {100 - 4} \right)$ We can observe that we can apply the identity $\left( {x + a} \right)\left( {x + b} \right) = {x^2} + \left( {a + b} \right)x + ab$Here $a = -5$ and $b = -4$
$\left( {100 - 5} \right)\left( {100 - 4} \right) = {\left( {100} \right)^2} + \left[ {\left( { - 5} \right) + \left( { - 4} \right)} \right]\left( {100} \right) + \left( { - 5} \right) \times \left( { - 4} \right)$
$= 10000 - 900 + 20$
$= 9120$ Therefore, we conclude that the value of the product $95 \times 96$ is $9120$
$95 \times 96{\text{ can also be written as}}\left( {100 - 5} \right)\left( {100 - 4} \right)$ We can observe that we can apply the identity $\left( {x + a} \right)\left( {x + b} \right) = {x^2} + \left( {a + b} \right)x + ab$Here $a = -5$ and $b = -4$
$\left( {100 - 5} \right)\left( {100 - 4} \right) = {\left( {100} \right)^2} + \left[ {\left( { - 5} \right) + \left( { - 4} \right)} \right]\left( {100} \right) + \left( { - 5} \right) \times \left( { - 4} \right)$
$= 10000 - 900 + 20$
$= 9120$ Therefore, we conclude that the value of the product $95 \times 96$ is $9120$
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