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# Evaluate using suitable identities:

(i) (48)²

(ii) 181² - 19²

(iii) 497 × 505

(iv) 2.07 × 1.93

**Solution:**

(i) (48)²

We can write (48)² as (50 - 2)²

We have (a - b)² = a² - 2ab + b²

Here a = 50 and b = 2

∴ (50 - 2)² = (50)² - (2 × 50 × 2) + (2)²

= 2500 - 200 + 4

= 2504 - 200

= 2304

(ii) 181² - 19²

We have the __identity__: a² - b² = (a - b) (a + b)

Here a = 181 and b = 19

∴ 181² - 19² = (181 - 19) (181 + 19)

= 162 × 200

= 32400

(iii) 497 × 505

We can write 497 × 505 as (500 - 3) (500 + 5)

Using the identity (x + a) (x + b) = x² + (a + b) x + ab

= 500² + [(-3 + 5) × 500] + [(-3) (5)]

= 250000 + 1000 - 15

= 250985

(iv) 2.07 × 1.93

We can write 2.07 × 1.93 as (2 + 0.07) (2 - 0.07)

Using the identity (a + b) (a - b) = a² - b²

Here a = 2 and b = 0.07

∴ (2 + 0.07) (2 - 0.07)

= 2² - (0.07)²

= 3.9951

**✦ Try This: **Evaluate using suitable identities: (i) 271² - 29², (ii) 294 × 306

(i) 271² - 29²

We have the identity: a² - b² = (a - b) (a + b)

Here a = 271 and b = 29

∴ 271² - 29² = (271 - 29) (271 + 29)

= 242 × 300

= 72600

(ii) 291 × 306

We can write 291 × 306 as (300 - 9) (300 + 6)

Using the identity (x + a) (x + b) = x² + (a + b) x + ab

= 300² + [(-9 + 6) × 300] + [(-9) (6)]

= 90000 - 900 - 54

= 89046

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 9

**NCERT Exemplar Class 8 Maths Chapter 7 Sample Problem 13**

## Evaluate using suitable identities: (i) (48)² (ii) 181² - 19² (iii) 497 × 505 (iv) 2.07 × 1.93

**Summary:**

Evaluating (i) (48)², (ii) 181² - 19², (iii) 497 × 505, (iv) 2.07 × 1.93, using identities we get 2304, 32400, 250985 and 3.9951 respectively

**☛ Related Questions:**

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