Question

$125 ^{3} + 1000 ^{3} \: use \: idendity$
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Answer 1

Calculations

Calculation of $125^3$ is as follows.

$125^3$

$=(100+25)^3$

$=100^3+3\times 100^2\times 25+3\times 100\times 25^2+25^3$

Calculation of $25^2$ is as follows.

$25^2$

$=(20+5)^2$

$=20^2+2\times 20\times 5+5^2$

$=\boxed{625}$

Now, calculation of $25^3$ is as follows.

$625\times 25=\boxed{15625}$

Hence in the first calculation, $125^3$ is

$100^3+75\times 100^2+1875\times 100\times +15625$

$=1000000+750000+187500+15625$

$=\boxed{1953125}$

Thus the required answer, $125^3+1000^3$ is $\boxed{1001953125}$.

More information

The number of zeros in $1000^3$ is $9$, because the power of $10$ is $9$.

Explanation: $(1000^3)^3=((10)^3)^3$

                    $=10^{3\times 3}=10^9$