**By using suitable identities, evaluate the following:**

#### (i) (103)^{3}

#### (ii) (99)^{3}

#### (iii) (10.1)^{3}

**Answer :**

**(i) (103)**^{3}

^{3}

It can be written as

= (100 + 3)^{3}

Expanding using formula

= 100^{3} + 3^{3} + 3 × 100 × 3 (100 + 3)

By further calculation

= 1000000 + 27 + 900 × 103

So we get

= 1000000 + 27 + 92700

= 1092727

**(ii) (99)**^{3}

^{3}

It can be written as

= (100 – 1)^{3}

Expanding using formula

= 100^{3} – 1^{3} – 3 × 100 × 1 (100 – 1)

By further calculation

= 1000000 – 1 – 300 × 99

So we get

= 1000000 – 1 – 29700

= 1000000 – 29701

= 970299

**(iii) (10.1)**^{3}

^{3}

It can be written as

= (10 + 0.1)^{3}

Expanding using formula

= 10^{3} + 0.1^{3} + 3 × 10 × 0.1 (10 + 0.1)

By further calculation

= 1000 + 0.001 + 3 × 10.1

So we get

= 1000 + 0.001 + 30.3

= 1030.301

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