Evaluate each of the following using suitable identities.
(1) $(104)^{3}$
(2) $(999)^{3}$

Open in App

Solution

(1) $(104)^{3} = (100 + 4)^{3}$ [Now $(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}]$

$= (100)^{3} + 3 (100)^{2} (4) + 3 (100) (4)^{2} + 4^{3}$

$= 1000000 + 3 \times 10000 \times 4 + 3 \times 100 \times 16 + 64$

$= 1000000 + 120000 + 4800 + 64$

$= 1124864$

(2) $(999)^{3} = (1000 - 1)^{3}$ $(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$

$= (1000)^{3} - 3 (1000)^{2} (1) + 3 (1000) (1)^{2} - (1)^{3}$

$= 1000000000 - 3 \times 1000000 + 3 \times 1000 - 1$

$= 997, 002, 999$

Suggest Corrections

Similar questions

(999)^{3}

{(103)}^{3}

{(99)}^{3}

Evaluate the following using suitable identities:

${(998)}^{3}$ [2 MARKS]

Using suitable identities, evaluate the following:

$(103)^{2}$

Question 86 (v)

Using suitable identities, evaluate the following:

$(1005)^{2}$

Join BYJU'S Learning Program