Question
Evaluate using suitable identity: ${\left( {99} \right)^3}$
✓
Answer
${\left( {99} \right)^3}$
${\left( {99} \right)^3}{\text{ can also be written as}}{\left( {100 - 1} \right)^3}.$
Using identity, ${\left( {x - y} \right)^3} = {x^3} - {y^3} - 3xy\left( {x - y} \right)$
${\left( {100 - 1} \right)^3} = {\left( {100} \right)^3} - {\left( 1 \right)^3} - 3 \times 100 \times 1\left( {100 - 1} \right)$
= 1000000-1-300(99)
= 999999-29700
= 970299.
${\left( {99} \right)^3}{\text{ can also be written as}}{\left( {100 - 1} \right)^3}.$
Using identity, ${\left( {x - y} \right)^3} = {x^3} - {y^3} - 3xy\left( {x - y} \right)$
${\left( {100 - 1} \right)^3} = {\left( {100} \right)^3} - {\left( 1 \right)^3} - 3 \times 100 \times 1\left( {100 - 1} \right)$
= 1000000-1-300(99)
= 999999-29700
= 970299.
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