Question

Without finding the cubes, factories (x-2y)³+(2y-z)³+(z-x)³​

Answer 1

Answer:

this is the answer for your question

Answer 2

GivEn:

• (x - 2y)³ + (2y - z)³ + (z - x)³

To find:

• Factors of (x - 2y)³ + (2y - z)³ + (z - x)³.

Solution:

☯ (x - 2y)³ + (2y - z)³ + (z - x)³

★ According to the Question:

We know that,

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

Here,

• a = (x - 2y)
• b = (2y - z)
• c = (z - x)

⠀━━━━━━━━━━━━━━━━━━━━━━━

➯ a + b + c = (x - 2y) + (2y - z) + (z - x) = 0

➯ 3(x - 2y)(2y - z)(z - x)

∴ Hence, Factorisation of (x - 2y)³ + (2y - z)³ + (z - x)³ is 3(x - 2y)(2y - z)(z - x).

⠀

⠀━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀★ Identities related to it :

• (a + b)²=a²+ 2ab + b² = (-a-b)²
• (a - b)2a² - 2ab + b²
• (a-b) (a + b) = a²-b²
• (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a+b-c)² - a² + b²+ c² + 2ab-2bc-2ca
• (a-b+c)² - a² + b² + c² - 2ab - 2bc +2ca
• (a+b+c)²=a² + b²+ c² - 2ab + 2bc-2ca
• (a-b-c)2- a² + b² + c² - 2ab + 2bc - 2ca
• (a+b)³ a³ + b³ + 3ab (a + b)
• (a-b)3a³-b³-3ab (a - b)
• a³ + b³ = (a + b)³-3ab(a + b)= (a + b) (a²- ab + b²)
• a³-b³(a - b)³ + 3ab(a - b)(a - b) (a² + ab + b²)
• a³ + b³ + c³-3abc = (a+b+c) (a²+ b² + c²-ab-bc-ca)