Question

13.
(7m - 5n)^3- (7m+5n)3 = ...
A) 1470m2n-250n3
c) -1470m^2n-250n^3
B) 1470m'n
D) -1470m?​

Answer 1

Given :- (7m - 5n)^3- (7m+5n)3 = ...

A) 1470m2n-250n3

B) -1470m^2n-250n^3

C) 1470m'n

D) -1470m

Solution :-

Let a = 7m and b = 5n .

using :-

• (a - b)³ = a³ - b³ - 3ab(a - b)
• (a + b)³ = a³ + b³ + 3ab(a + b)

so,

→ (a³ - b³ - 3a²b + 3ab²) - (a³ + b³ + 3a²b + 3ab²)

→ a³ - a³ - b³ - b³ - 3a²b - 3a²b + 3ab² - 3ab²

→ - 2b³ - 6 a²b

→ - (2b³ + 6a²b)

→ - [2*(5n)³ + 6(7m)² * (5n)]

→ -[2*125n³ + 6*49m²*5n]

→ -[250n³ + 1470m²n]

→ - 1470m²n - 250n³ (B) (Ans.)

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if a²+ab+b²=25

b²+bc+c²=49

c²+ca+a²=64

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Answer 2

Given : (7m - 5n)³- (7m+5n)³

To Find : Simplified Value

A) 1470m²n-250n³

c) -1470m²n-250n³

B) 1470m²n

D) -1470m³​

Solution :

(7m - 5n)³- (7m+5n)³

a³ - b³  = ( a - b)(a²  + b² + ab)

a = 7m - 5n

b = 7m + 5n

a - b =  7m - 5n - (7m + 5n)  = - 10 n

a²  + b² + ab

= (7m - 5n)² +  (7m+5n)²  +  (7m - 5n) (7m + 5n)

(x + y)² = x² + y² + 2xy

(x - y)² = x² + y² - 2xy

(x - y)(x + y)  = x² - y²

x = 7m   and y  = 5n

 x² + y² + 2xy + x² + y² - 2xy +  x² - y²

= 3x² + y²

= 3(7m)² + (5n)²

= 147m² + 25n²

(7m - 5n)³- (7m+5n)³  = (-10n) (147m² + 25n²)

= - 1470m²n - 250n³

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