Simplify (5a+3b)³-(5a-3b)³
Answers
(5a+3b)³-(5a-3b) = 450a²b + 54b³
Given:
(5a+3b)³- (5a-3b)³
To find:
Simplify (5a+3b)³-(5a-3b)
Solution:
As we know from Algebraic identities
(a+b)³ = a³+3a²b+3ab²+b³
(a-b)³ = a³- 3a²b+3ab²-b³
Take a = 5a, b = 3b and apply the formula for (5a+3b)³ and (5a-3b)³
(5a+3b)³ = (5a)³+3(5a)²(3b) + 3(5a)(3b)²+(3b)³
= 125a³+ 9b(25a²) +15a(9b²) + 27b³
= 125a³ + 225a²b + 135ab² + 27b³
(5a+3b)³ = 125a³ + 225a²b + 135ab² + 27b³ .........(1)
(5a-3b)³ = (5a)³ - 3(5a)²(3b) + 3(5a)(3b)²- (3b)³
= 125a³ - 9b(25a²) +15a(9b²) - 27b³
= 125a³ - 225a²b + 135ab² - 27b³
(5a-3b)³ = 125a³ - 225a²b + 135ab² - 27b³ ..........(2)
From (1) and (2)
5a+3b)³-(5a-3b)
= 125a³ + 225a²b + 135ab² + 27b³ - (125a³ - 225a²b + 135ab² - 27b³)
= 125a³ + 225a²b + 135ab² + 27b³ - 125a³ +225a²b - 135ab² +27b³
= 225a²b + 27b³ +225a²b +27b³
= 450a²b + 54b³
Therefore, (5a+3b)³-(5a-3b) = 450a²b + 54b³
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