Question

If p-q=r, prove that, p3-q3-r3=3pqr

Answer 1

Answer:

Proved below.

Step-by-step explanation:

Given,

    p - q = r

Cube on both sides:

⇒ ( p - q )^3 = r^3

⇒ p^3 - q^3 - 3pq( p - q ) = r^3

⇒ p^3 - q^3 - 3pq( r ) = r^3          { from above, p - q = r }

⇒ p^3 - q^3 - 3qpr = r^3

⇒ p^3 - q^3 - r^3 = 3pqr

      Proved.