Question

198×209 use identities​

Answer 1

Step-by-step explanation:

198×209

(200-2)(200+9)

(200)^2+(9-2)200+9 x -2

40000+700-18

40682..........xD

Answer 2

The value of $\bf 198 \times 209 = 41382$

Given:

• $198 \times 209$

To find:

• Solve using Identity.

Solution:

Identity to be used:

$\bf (x - a)(x + b) = {x}^{2} + x(b - a) - ab$

Step 1:

Write the given number so that we can apply Identity.

$198 \times 209 = (200 - 2) \times (200 +9 )$

Step 2:

Apply identity.

It is clear that

$x = 200$

$a = 2 \\ b = 9$

So,

$(200 - 2)(200 + 9) = {(200)}^{2} + 200(9 - 2) - 2 \times 9$

or

$(200 - 2)(200 + 9) = 40000 + 1400 - 18$

or

$(200 - 2)(200 + 9) = 41400 - 18$

or

$(200 - 2)(200 + 9) = 41382$

Thus,

$\bf \red{198 \times 209 = 41382}$

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