Question

plz help me to understand this question give answer stap by stap.​

Answer 1

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Factories it

(5a - 7b)³ + (9c - 5a)³ + (7b - 9c)³

ร๏ℓนт¡๏ภ

→ (5a - 7b)³ + (9c - 5a)³ + (7b - 9c)³

★ Applying identity :

(a - b)³ = a³ - b³ - 3ab(a - b)

→ [(5a)³ - (7b)³ - 3*5a*7b(5a - 7b)]+[(9c)³ - (5a)³ - 3*9c*5a(9c - 5a)]+[(7b)³ - (9c)³ - 3*7b*9c(7b - 9c)]

→ [125a³ - 343b³ - 105ab(5a - 7b)]+[729c³ - 125a³ - 135ac(9c - 5a)]+[343b³ - 729c³ - 189bc(7b - 9c)]

→ [125a³ - 343b³ - 525a²b + 735ab²]+[729c³ - 125a³ - 1215ac² + 675a²c]+[343b³ - 729c³ - 1323b²c + 1701bc²]

→ 125a³ - 343b³ - 525a²b + 735ab² + 729c³ - 125a³ - 1215ac² + 675a²c + 343b³ - 729c³ - 1323b²c + 1701bc²

**Combine like terms**

→ 125a³ - 125a³ - 343b³ + 343b³ + 729c³ - 729c³- 525a²b + 735ab² - 1215ac² + 675a²c - 1323b²c + 1701bc²

→ -525a²b + 735ab² - 1215ac² + 675a²c - 1323b²c + 1701bc²

Answer 2

ғᴀᴄᴛᴏʀɪsᴇ:-

(5a - 7b) ³ + (9c - 5a) ³ + (7b - 9c) ³

This is in the form of identity :-

➦ a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - ac - bc)

But we also know that,

➦ If a + b + c = 0 , then a³ + b³ + c³ = 3abc

From the question we get,

➭ a = (5a - 7b)

➭ b = (9c - 5a)

➭ c = (7b - 9c)

So now,

➭ ( a + b + c) = ( 5a - 7b) + (9c - 5a) + (7b - 9c)

➭ 5a - 5a - 7b + 7b + 9c - 9c

➭ 0

Hence,

➦ a³ + b³ + c³ = 3abc

So,

➠ ( 5a - 7b)³ + (9c - 5a) ³ + (7b - 9c) = 3 (5a - 7b) (9c - 5a) (7b - 9c)

➠ 3 ×( 45ac - 25a² - 63bc + 35ab) (7b - 9c)

➠ 3 × (315abc - 175a²b - 441b²c + 245ab² - 405ac² + 225a²c + 567bc² - 315abc )

➠ 3 × (175a²b - 441b²c + 245ab² - 405ac² + 225a²c + 567bc²)

➠ - 525a²b - 1323b²c + 735ab² - 1215ac² + 675a²c + 1701bc²