Question

evaluate 993³ and 1002³ by using algebraic identies

Answer 1

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Answer 2

Concept Introduction:

$(a+b)^{3} =a^{3} +b^{3}+3ab(a+b)$

$(a-b)^{3} =a^{3} -b^{3}-3ab(a-b)$

Given: $993^{3}$ and $1002^{3}$

To Find:

We have to find the value of, $993^{3}$ and $1002^{3}$ by using algebraic identities.

Solution:

According to the problem,

a) $993^{3}$ = $(1000-7)^{3} =1000^{3} -7^{3} -3*1000*7(1000-7)=1000000000-343-21000*993$

$=1000000000-343-20853000=979146657$

b) $1002^{3}$= $(1000+2)^{3} =1000^{3} +2^{3} +3*1000*2(1000+2)=1000000000+8+6000*1002$

$=1000000000+8+6012000=1006012010$

Final Answer:

The value of $993^{3}$  is $979146657$ and  $1002^{3}$ is $1006012010$.

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