Question

evaluate using identities 103*97

Answer 1

↑ Here is your answer ↓ _____________________________________________________________ _____________________________________________________________

$103 * 97$

$(100+3)(100-3)$

$100^2 - 3^2$

$10000-9$

$9991$

Answer 2

Value of 103×97 is 9991.

Given:

• Two numbers
• 103 and 97

To find:

• Evaulate 103×97 using Identity.

Solution:

Identity to be used:$\bf (x - y)(x + y) = {x}^{2} - {y}^{2}$

Step 1:

Write number like given identity.

$103 = 100 + 3 \\ 97 = 100 - 3$

Step 2:

Apply in identity.

$103 \times 97 = (100 + 3) \times (100 - 3)$

or

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

or

$(100 + 3) \times (100 - 3) = 10000 - 9$

or

$(100 + 3) \times (100 - 3) = 9991$

Thus,

$\bf 103 \times 97 = 9991$

Learn more:

1) Using (x + a) (x + b) = x^2 + (a + b) x + ab, find (i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8

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2) Find the product of 4567 x 99 using suitable property.

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