Question

Using the identity evaluate the following
1001³

Answer 1

Hey mate! here is your answer,

As we know algebraic expression:

$(a + b) {}^{2} = a {}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3} \\ or \\ (a + b) {}^{3 } = a {}^{3} + {b}^{3 } + 3ab(a + b) \\ \\ now \\ (1001) {}^{3} \\ = (1000 + 1) {}^{3} \\ = (1000) {}^{3} + {1}^{3} + 3 \times 1000 \times 1(1000 + 1) \\ = 1000000000 + 1 + 3000 \times 1001 \\ = 1000000000 + 1 + 3003000 \\ = 1003003001$

Hope this will help you.

Give thanks if useful.