Question

Q: 13 Use an appropriate identity to evaluate (100 x 100) - (98 x 98).​

Answer 1

Answer:

Using the identity (x+a)(x+b) = x

2

+(a+b)x+ab

Writing 102 as 100+2 and 98 as 100−2

Hence (100+2)(100−2) = 100

2

+[2+(−2)]100+(2)(−2)

= 10000+(0)100−4

= 9996

The answer is 9996

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Answer 2

$(100 \times 100) - (98 \times 98)$

${(100)}^{2} - {(98)}^{2}$

It is In the form of a²-b² .

Now using the identity ,

a² - b² = ( a + b ) ( a - b )

Therefore ,

${(100)}^{2} - {(98)}^{2} = (100 + 98)(100 - 98)$

$198 \times 2$

$396$

Hence , The required answer is 396.