Question

Using suitable identities, evaluate the following.i) 98×103 ii) (9.9)² iii) 9.8×10.2 iv) (339)²-(161)²​

Answer 1

Answer:

(I) 98 x 103 = {100-2} {100+3} =100 {100+3} -2{100+3} = 10000+300-200-6 = 10300-206 = 10094

(II) (9.9)² = (10-0.1)² = 10²+ (0.1)²- 2x10x0.1 = 100+0.01-2 = 98.01 { (a-b)²=a²+b²-2ab }

(III) 9.8x10.2 = {10-0.2} {10+0.2} = 10²-(0.2)² = 100 -0.04 = 99.96 { (a+b) (a-b) = a²-b² }

(IV) (339)²-(161)² = (339-161) (339+161) = 178x500 = 89000 {a²-b² = (a+b) (a-b) }

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Answer 2

Answer:

1. 10094
2. 98.01
3. 99.96
4. 89000

Step-by-step explanation:

1). (100-2)(100+3)=(100)^2+(-2+3)100+(-2)×3

=10000+100-6=10094

{(x+a) (x+b) =x^2+(a+b) x+ab}

2). (9+0.9) ^2= (9)^2+2(9) (0.9) +(0.9) ^2

=81+16.2+0.81=98.01

{(a+b)^2=a^+2ab+b^2}

OR

{(a-b) ^2=a^2-2ab+b^2}

(10-0.1) ^2=(10)^2-2(10) (0.1) +(0.1) ^2

=100-2+0.01=98.01

3).(10-0.2) (10+0.2) =(10) ^2-(0.2) ^2

=100-0.04=99.96

{(a+b) (a-b)= a^2-b^2}

4). (339+161)(339-161) =500×178

=89000

{a^2-b^2=(a+b) (a-b)^2}