Question

Evaluate of the following using suitable identites (1001)³​

Answer 1

Solution -

• $\sf\green{(1001)^3}$

Identity to be used -

$\huge{\boxed{\sf{\orange{(a + b)^3 = a^3 + b^3 + 3ab(a + b)}}}}$

↬ (1001)³

↬ $\sf{(1000 + 1)^3}$

↬ $\sf{(1000)^3 + (1)^3 + 3 \times 1000 \times 1(1000 + 1)}$

↬ $\sf{1000000000 + 1 + 3000(1001)}$

↬ $\sf{1000000000 + 1 + 3003000}$

↬ $\sf{1,003,003,001}$

$\LARGE{\boxed{\sf{\red{Answer = 1,003,003,001}}}}$

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Some useful identities -

• $\sf\green{{(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}$

• $\sf\green{{(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}$

• $\sf\green{(a - b)^3 = a^3 - b^3 - 3ab(a - b)}$

Signs are changed on the following bases -

• (-) (-) = (+)

• (+) (+) = (+)

• (-) (+) = (-)

• (+) (-) = (-)