Question

102×103 solve using identity

Answer 1

Heya !!!

This is your answer....

Given :---

102 × 103.

We have to solve it using a suitable identity.....

So......

102 × 103
= (100 + 2) (100 + 3) (i)

By looking at it, we can say that the identity which will we use here will....
(x +a)(x +b) = x^2 + (a+b)x + ab (ii)


By comparing (i) and (ii), we can say that
x = 100
a = 2, and
b = 3

Therefore, using the identity .....
102×103
= (100+2) (100+3)
= 100^2 + (2+3)100 + 2×3
= 10000 + 600 + 6
= 10606.

Hence, your answer is 10606.

Hope it helps..

.....

Answer 2

102 × 103 = 10506

Given :

The expression 102 × 103

To find :

The product using suitable identity

Formula :

We are aware of the identity that

$\displaystyle \sf{(y + a)(y + b) = {y}^{2} + (a + b)y + ab }$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is 102 × 103

Step 2 of 2 :

Find the product

We are aware of identity that

$\displaystyle \sf{(y + a)(y + b) = {y}^{2} + (a + b)y + ab }$

We take y = 100 , a = 2 , b = 3

Thus we get

$\displaystyle \sf{ 102 \times 103 }$

$\displaystyle \sf{ = (100 + 2 )\times (100 + 3 )}$

$\displaystyle \sf{ = {(100)}^{2} + (2 + 3) \times 100 + (2 \times 3)}$

$\displaystyle \sf{ = 10000 + (5 \times 100) + 6}$

$\displaystyle \sf{ = 10000 + 500 + 6}$

$\displaystyle \sf{ = 10506}$

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