Question

using suitable identity find value of (.99)²​

Answer 1

An identity is true only for certain values of its variables. An equation is not an identity.

The following are the identities

(a + b)² = a² + 2ab + b² 

(a – b)² = a² – 2ab + b² 

(a – b)(a + b) = a² – b²

 Another useful identity is

 (x + a) (x + b) = x² + (a + b) x + ab

If the given expression is the difference of two squares we use the formula

a² –b² = (a+b)(a-b)

 

• The above four identities are useful in carrying out squares and products of algebraic expressions. They also allow easy alternative methods to calculate products of numbers and so on.

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Solution:

1) 99²

= (100 -1)²

= 100²- 2×100×1 + 1²               [(a – b)² = a² – 2ab + b² ]

= 10000 - 200 + 1

= 9801

Answer 2

9801 is the correct option.

Expansion of

$(99)^{2}$

using identities:-

Firstly,

Expand

$(99)^{2}$

In the form of

$(a - b)^{2}$

Now the expansion of this identify is

$a^{2} + b^{2} - 2ab$

So Now,

The expansion will be:-

$(100 - 1)^{2}$

Now expand this using the expansion of the identity:-

$100^{2} + 1^{2} - 2(100)(1)$

The value of this will be:

10000+1-200

=10001-200

=9801

So, with this procedure 9801 will be the answer for the same.

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