Question

help to do this it's urgent​

Answer 1

Answer:

A

Step-by-step explanation:

3 (a+b) (b +c) (c+a) (a-b) (b-c) (c-a).

Answer 2

Question:-

The value of (a² - b²)³ + (b² - c²)³ + (c² - a²)³ is

Formula Used:-

• x³ + y³ + z³ -3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)
• and when (x + y + z) = 0, x³ + y³ + z³ = 3xyz [as because of (x + y + z) being 0, the full RHS becomes 0, and then x³ + y³ + z³ - 3xyz = 0, => x³ + y³ + z³ = 3xyz]
• (m² - n²) = (m + n)(m - n)

Answer:-

(a² - b²)³ + (b² - c²)³ + (c² - a²)³

Let (a² - b²) be x, (b² - c²) be y and (c² - a²) be z

So we have the expression,

x³ + y³ + z³

And x + y + z = (a² - b²) + (b² - c²) + (c² - a²) = 0

So we have x + y + z = 0

So, by second formula given above,

x³ + y³ + z³ = 3xyz

And we have assumed (a² - b²) to be x, (b² - c²) to be y and (c² - a²) to be z, so putting the values

(a² - b²)³ + (b² - c²)³ + (c² - a²)³ = 3(a² - b²)(b² - c²)(c² - a²)

This can be further factorised by using the third formula given above

3(a² - b²)(b² - c²)(c² - a²)

= 3(a + b)(a - b)(b + c)(b - c)(c + a)(c - a)

= 3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a)

Ans. (a² - b²)³ + (b² - c²)³ + (c² - a²)³ = 3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a)