Question

Q.II A] Solve the following :-
1) Expand:- [Any 2]
a) (9x - 5t)(9x+4t)
b) (52)3
() (198)3​

Answer 1

Answer:

a] (9x - 5t)(9x + 4t)

Using Identity here-

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

⇒ (9x - 5t)(9x + 4t)

⇒ (9x)² + 9x (5t - 4t) - 5t * 4t

⇒ 81x² + 9xt - 20t²

_______________________

b] (52)³

It can be written as -

(50 + 2)³

Using identity here ;

$\boxed{ \sf (a + b) {}^{3} = a {}^{3} + b {}^{3} + 3ab(a + b)}$

⇒ (50 + 2)³

⇒ (50)³ + (2)³ + 3 * 50 * 2 (50 + 2)

⇒ 125,000 + 8 + 300 * 52

⇒ 125,008 + 15,600

⇒ 140,608

_______________________

c] (198)³

It can be written as -

(200 - 2)³

Using identity here -

$\boxed{ \sf (a - b)^{3} = a {}^{3} - b {}^{3} - 3ab(a - b)}$

⇒ (200 - 2)³

⇒ (200)³ - (2)³ - 3 * 200 * 2 (200 - 2)

⇒ 8,000,000 - 8 - 1200 * 198

⇒ 7,999,992 - 237,600

⇒ 7,762,392

_______________________

Answer 2

HeRe Is Your Ans ⤵

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1 =>

➡81X² + 36XT - 45TX - 20T²

➡81X² - 20T² - 9XT

2 =>

➡(50 + 2)³ = 50³ + 2³ + 3 × (50)² × 2 + 3 × 50 × (2)²

➡125000 + 8 + 3 × 2500 × 2 + 150 × 4

➡125008 + 15000 + 600

➡140608

3 =>

➡(195 + 3)³ = 195³ + 3³ + 3 × (195)² × 3 + 3 × 195 × (3)²

➡7414875 + 27 + 3 × 38025 × 3 + 3 × 195 × 9

➡7414902 + 342225 + 5265

➡7762392

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