Question

Using he identity (a-b)2 = (a2-2ab+b2)
Evaluate:
(192)2
step by step explanation
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Answer 1

Answer:

(192)² is 36864.

Step-by-step explanation:

We have,

• (192)²

We can also write this as :

• (200 - 8)²

We have to use the identity : (a - b)² = a² - 2ab + b²

Here,

a is 200 and b is 8.

Put a and b in Identity :

→ (200 - 8)²

→ (200)² - 2 × 200 × 8 + (8)²

→ 40000 - 3200 + 64

→ 36800 + 64

→ 36864

Thus,

(192)² is 36864 .

Know some more algebraic identities :

1. (a + b)² = a² + 2ab + b².
2. a² - b² = (a + b) (a - b).
3. (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.
4. (a - b - c)² = a² + b² + c² - 2ab + 2bc - 2ca.
5. (a + b)³ = a³ + b³ + 3ab(a + b).
6. (a - b)³ = a³ - b³ - 3ab(a - b)
7. a³ - b³ = (a - b)(a² + b² + ab)
8. a³ + b³ = (a + b)(a² + b² - ab)

Answer 2

Answer:

36,864

Step-by-step explanation:

Appropriate Question :

Using the identity (a - b)² = (a² - 2ab + b²)

Evaluate : (192)²

Solution :

Using the identity :

⇒ (a - b)² = (a² - 2ab + b²)

192² can be written as : (200 - 8)²

⇒ (200 - 8)²

Using the identity,

⇒ (200)² - 2(200)(8) + (8)²

⇒ (200 × 200) - (2 × 200 × 8) + (8 × 8)

⇒ 40000  - 3200 + 64

⇒ 40000 - 3136

⇒ 36, 864

⊕ Hence, (192)² = 36, 864

More to Know :

More algebric identities :

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab

Note :

The above question can also be solved using (a + b)² = a² + 2ab + b² identity as well. It's shown below :

It can be written as :

⇒ (190 + 2)²

⇒ (190)² + 2(190)(2) + (2)²

⇒ 36,100 + 760 + 4

⇒ 36,864