Question

factorize (p-q)^3 + (q-r)^3 +(r-p)^3

Answer 1

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Answer 2

Answer :

Let us take,

x = p - q, y = q - r and z = r - p

Now, x + y + z

= p - q + q - r + r - p

= 0

We know that,

x³ + y³ + z³ - 3xyz

= (x + y + z) (x² + y² + z² - xy - yz - zx)

⇒ (p - q)³ + (q - r)³ + (r - q)³

- 3 (p - q) (q - r) (r - p)

= 0 × (x² + y² + z² - xy - yz - zx)

⇒ (p - q)³ + (q - r)³ + (r - q)³

= 3 (p - q) (q - r) (r - p),

which is the required factorization

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