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  • Using suitable identity, evaluate the following (i)103^{3}\\ (ii)101 \times 102\\ (iii)999^{2}

Using suitable identity, evaluate the following

     \\(i)103^{3}\\ (ii)101 \times 102\\ (iii)999^{2}

Answers (1)

(i) 1092727

Solution

Given,

\\(103)^{3}=(100+3)^{3}\\ =100^{3}+3^{3}+3(100)^{2}(3)+3(100)(3)^{2}\; \; \; (using \; (a+b)^{3}=a^{3}+b^{3}+3a^{2}b+3ab^{2})\\ =1000000+27+90000+2700\\ =1092727

Hence the answer is 1092727

(ii) 10302

Solution
Given, 101 \times 102=(100+1)(100+2)           

Using  (x+a)(x+b)=x^{2}+(a+b)x+ab 

Put x = 100, a = 1, b = 2
(100+1)(100+2)=100^{2}+(1+2)100+(1)(2)\\ =10000+300+2\\ =10302

Hence the answer is 10302

(iii)998001

Solution

Given, (999)^{2}=(1000-1)^{2}\\

Using (a-b)^{2}=a^{2}+b^{2}-2ab  

Putting a = 1000, b = 1
\\(1000-1)^{2}=(1000)^{2}+(1)^{2}-2(1000)(1)\\ =1000000+1-2000\\ =998001

Hence the answer is 998001.

 

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infoexpert24

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