Question

Evaluate using identies (1001)³


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Answer 1

Answer:

1003003001

Step-by-step explanation:

(1001)^3

(1000+1)^3

1000^3+3*1000^2*1+3*1000*1^2+1^3

1000000000+3*1000000+3*1000+1

1000000000+3000000+3000+1

=1003003001

Answer 2

Answer:

$1001 = 1000 + 1 \\ \\ (1001) {}^{3} = (1000 + 1) {}^{3}$

We know,

$(x + y) {}^{3} = x {}^{3} + y {}^{3} + 3xy(x + y)$

Therefore,

$(1000 +1 ) {}^{3} = 1000 {}^{3} + 1 {}^{3} + 3 \times 1000 \times 1(1001) \\ \\ = 1003003001</p><p></p><p>$