Question

the value of 99²-98² is
​

Answer 1

Answer:

The value of $(99)^{2} -(98)^{2}$ is 197.

Step-by-step explanation:

Given a series, $(99)^{2} -(98)^{2}$

Writing 99 as 98 + 1, the series can be rewritten as

$(98+1)^{2} -(98)^{2}$                                                                        ...(1)

Using the algebraic identity, $(a+b)^{2} =(a)^{2}+(b)^{2}+2ab$.

Equation (1) can be expanded as

$(98)^{2}+1^{2} +2\times 98\times 1-(98)^{2}$

Cancelling out the positive and negative $(98)^{2}$, we get

$=1^{2} +2\times 98\times 1$

$=1 +196=197$

Hence, the value of $(99)^{2} -(98)^{2}$ is 197.