Question

evaluate the following by using suitable identity ( )
a) 202 x 205 b) 99^2​

Answer 1

Step-by-step explanation:

Given:-

a) 202 x 205 b) 99^2

To find:-

Evaluate the following by using suitable identity

a) 202 x 205 b) 99^2

Solution:-

a)

Given numerical expression is 202×205

It can be written as (200+2)×(200+5)

It is in the form of (x+a)(x+b)

Here, x=200;a=2;b=5

We know that (x+a)(x+b)=x²+(a+b)x+ab

(200+2)×(200+5)

=>(200)²+(2+5)(200)+(2×5)

=>40000+(7)(200)+10

=>40000+1400+10

=>41410

Therefore,202×205=41,410

_______________________________

b)

Given that: 99²

It can be written as (100-1)²

It is in the form of (a-b)²

Here,a=100;b=1

We know that

(a-b)²=a²-2ab+b²

(100-1)²=(100)²-2(100)(1)+(1)²

=>99²=10000-200+1

=>99²=10001-200

=>99²=9801

Therefore,99²=9801

______________________________

Answer:-

a)202×205=41,410

b)99²=9801

Using formulae:-

• (x+a)(x+b)=x²+(a+b)x+ab
• (a-b)²=a²-2ab+b²