Question

Solve the following using brackets
98×102
67×210
105×95
58×1001

Answer 1

Answer :

Given :

$\longrightarrow{98 \times 102 }$

$\longrightarrow{67 \times 210}$

$\longrightarrow{105 \times 95}$

$\longrightarrow{58 \times 1001}$

Required to Find :

1. The product of the Numbers .

Mentioned Condition :

$\boxed{\Rightarrow{\textsf{Solve using brackets}}}$

Explanation :

In the question they given us some numbers and asked us to find the product of them using brackets .

To solve this question we need to convert them into brackets by splitting them to nearest rough figure this rough figure should be divisible by 5 and 10

For example ;

48 x 52

This is splited as ;

(50 - 2) (50 + 2)

This is the way in which they have to be splited with brackets .

Now, let's crack the above question .

Solution :

➊

$\longrightarrow{98 \times 102 }$

These numbers are spilted as ;

$\longrightarrow{(100 - 2) (100 + 2)}$

The above is actually representing an identity

That is ;

$\boxed{(x + y)(x - y) = {x}^{2} - {y}^{2}}$

Using this we can find the product ;

Here, x = 100 , y = 2

$\longrightarrow{{100}^{2} - {2}^{2}}$

$\longrightarrow{10000\:-\:4}$

$\implies{9996}$

Hence Answer is ,

$\boxed{\large{9996}}$

$\rule{400}{2}$

➋

$\longrightarrow{67 \times 210}$

These numbers are spilted as ;

$\longrightarrow{(60+7) (200 + 10)}$

Now multipy them

$\longrightarrow{60(200 + 10)+7(200 + 10)}$

$\longrightarrow{12000 + 600 + 1400 + 70 }$

$\implies{14070}$

Hence Answer is ,

$\boxed{\large{14,070}}$

$\rule{400}{2}$

➌

$\longrightarrow{105 \times 95}$

These numbers are spilted as ;

$\longrightarrow{(100+5) (100 - 5)}$

The above is actually representing an identity

That is ;

$\boxed{(x + y)(x - y) = {x}^{2} - {y}^{2}}$

Using this we can find the product ;

Here, x = 100 , y = 5

$\longrightarrow{{100}^{2} - {5}^{2}}$

$\longrightarrow{10000\:-\:25}$

$\implies{9975}$

Hence Answer is ,

$\boxed{\large{9975}}$

$\rule{400}{2}$

➍

$\longrightarrow{58 \times 1001}$

These numbers are spilted as ;

$\longrightarrow{(60-2) (1000+1)}$

Now multipy them

$\longrightarrow{60(1000+1)-2(1000 + 1)}$

$\longrightarrow{60000+ 60 - 2000 - 2 }$

$\implies{58058}$

Hence Answer is ,

$\boxed{\large{58058}}$

$\rule{400}{2}$

✅ Hence Solved