Question

Solve using identity
$a)(9 {6})^{2} \\ b)(23 {1})^{2} - 13 {1}^{2} \\ c)18 {1}^{2} - 1 {9}^{2}$
solve step by step.​

Answer 1

Answer:

9216, 36200, 32400

Step-by-step explanation:

a) (96)²

We can write this as :

→ (100 - 4)²

Identity : (a - b)² = a² - 2ab + b²

Here, a = 100, b = 4

→ (100)² - 2(100)(4) + (4)²

→ 10000 - 800 + 16

→ 10016 - 800

→ 9216

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b) (231)² - (131)²

Identity : a² - b² = (a + b)(a - b)

Here, a = 231, b = 131

→ (231 + 131)(231 - 131)

→ (362)(100)

→ 36200

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c) (181)² - (19)²

Identity : a² - b² = (a + b)(a - b)

Here, a = 181, b = 19

→ (181 + 19)(181 - 19)

→ (200)(162)

→ 32400

Other identities which are frequently used :

• (a + b)² = a² + 2ab + b²

• (a + b)² - (a - b)² = 4ab

Answer 2

||✪✪ QUESTION ✪✪||

1) 96²

2) 231² - 131²

3) 181² - 19²

|| ✰✰ ANSWER ✰✰ ||

✭ Solution ⓵ :---

96 can be written as (90+6) or (100-4)

Lets solve both ,

➳ (96)²

➳ (90+6)²

using (a+b)² = a² + b² + 2ab now,

➳ (90)² + (6)² + 2*90*6

➳ 8100 + 36 + 1080

➳ 9216 (Ans).

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Also,

➺ (96)²

➺ (100-4)²

using (a-b)² = a² + b² - 2ab

➺ (100)² + (4)² - 2*100*4

➺ 10000 + 16 - 800

➺ 9216 (Ans).

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Also, Lets Try to solve it Directly Now,

➪ (96)² = (ab)² [ assume a as 9, and b as 6 ]

Than,

☛ (ab)² = [a²b²] + 20ab

So,

☞ (96)²

☞ (9²6²) + 20*9*6

☞(8136) + 1080

☞ 9216 (Ans).

[ This is the Trick To solve Square of Any Number . ]

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✭ Solution ❷ :-

⟼ (231)² - (131)²

Using (a² - b²) = (a+b)(a-b)

⟼ (231 + 131)(231-131)

⟼ 362 * 100

⟼ 36200 (Ans).

_____________

Now , Lets Try to Solve it in a Different way also, ,

231 can be written as (100+131)

So,

⤕ (231)² - (131)²

⤖ (100+131)² - (131)²

Now, using (a+b)² in first part

⤖ (100)² + (131)² + 2*131*100 - (131)²

As we can see (131)² will be cancel ,

So,

⤖ 10000 + 26200

⤖ 36200 (Ans).

______________________________

✭ Solution ⓷ :-

181² - 19²

Again , using (a+b)(a-b) = a² - b² ,

⟿ (181+19)(181-19)

⟿ 200 * 162

⟿ 32400 (Ans).

_________

Lets Think Differently now,

181 can be written as (200 - 19)

So,

➾ (181)² - (19)²

➾ (200-19)² - (19)²

Using (a-b)² = a² + b² - 2ab in First part we get,

➾ [ 200² + 19² - 2*200 * 19] - (19)²

Now, as we can see , (19)² will be cancel,

we get,

➾ 40000 - 7600

➾ 32400 (Ans).

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❦❦ Mathematics is Fun when we play with Numbers. ❦❦