Question

Evaluate the following using suitable identity
$(99)^{3}$
​

Answer 1

Step-by-step explanation:

$\bf \huge \underline{\underline{Question}} \:$

Evaluate the following using suitable identity$\tt. (99)^{3}$

$\bf \huge \underline{\underline{solution}} \:$

We known that:-

$\tt. (a+b)^3=a^3+b^3+3ab(a+b)and(a-b)^3=a^3-b^3-3ab(a-b)$

$\tt \: {99}^{3} = 100 - {1}^{3} \\ \\ \tt {100}^{3} - {1}^{3} \times 100 \times 1 \times 100 - 1$

$\tt. = 1000000 -1 -300(99)$

$\tt. = 1000000 - 1-29700$

$\tt. = 970299$

Answer 2

$\Huge{\red{\underline{\textsf{Question}}}}$

Evaluate the following using suitable identity

$\leadsto$$\rm(99)^{3}$

$\rule{300}2$

$\Huge{\orange{\underline{\textsf{Answer}}}}$

We write, $\rm 99 = 100 - 1$

$\mapsto$$\rm (99)^{3} = ( 100 - 1 )^{3}$

$\mapsto$$\rm ( 100 )^{3} - 1^{3} - 3( 100 ) ( 1 )( 100 - 1 )$

$\mapsto$$\rm 1000000 - 1 - 300( 99 )$

$\mapsto$$\rm 1000000 - 1 - 29700$

$\mapsto$$\rm 970299$

$\rule{300}2$