Question

Subtract the square of 99 from the square of 100 without actually calculating the squares. ​

Answer 1

Answer:

Given,

We need to Subtract the square of 99 from the square of 100 without actually calculating the squares.

Using the formula

${x}^{2} - {y}^{2} = (x + y)(x - y)$

We get....

$= > {(100)}^{2} - {(99)}^{2} \\ = > (100 + 99)(100 - 99) \\ = > 199 \times 1 \\ = > 199.$

Answer 2

Answer:

Your Question :---

Subtract 99² from 100² without actually calculating the squares.

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We know that ,

(a²-b)² = (a+b)(a-b)

so,

let a = 100 and b = 99 and putt values in above formula , we get,

(100²-99²) = (100+99)(100-99)

(100²-99²) = (199)(1)

(100²-99²) = 199 (Ans)

Some additional formulas you must aware of :-----

[1] ( a + b )² = a² + 2ab + b²

[2] ( a – b )² = a² – 2ab + b²

[3] ( a + b )³ = a³ + 3a² b + 3ab² + b³

[4] ( a – b )³ = a ³ – 3a² b + 3ab² – b³

[5] ( a + b )( a ² - ab + b² ) = a³ + b³

[6] ( a – b )( a ² + ab + b² ) = a³ – b³