Question

Evaluate 993^2 using algebraic identities

Answer 1

Given data : Evaluate 993² by using algebraic identities.

Solution : Here, we know :

⟹ 993 = { 1000 - 7 }

So we can write;

⟹ 993² = { 1000 - 7 }²

Now, by algebraic identity :

a² - 2ab + b²

Where, a = 1000 & b = 7

⟹ 993² = 1000² - 2 * 1000 * 7 + 7²

⟹ 993² = 1000000 - 2000 * 7 + 49

⟹ 993² = 1000000 - 14000 + 49

⟹ 993² = 986000 + 49

⟹ 993² = 986049

Answer : Hence, 993² is equal to 986049.

Answer 2

${(993)}^{2} \\ = {(1000 - 7)}^{2} \\ = {1000}^{2} + {7}^{2} - 2 \times 1000 \times 7 \\ = 1000000 + 49 - 14000 \\ = 986049$

The formula is

${(a - b)}^{2} = {a}^{2} \: + {b}^{2} - 2ab$

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