Question

( p + q )⁴ - ( p - q )⁴ = 8pq ( p² + q² )​

Answer 1

Solution :

Now,

L.H.S. = (p + q)^4 - (p - q)^4

= {(p + q)²}² - {(p - q)²}²

= {(p + q)² + (p - q)²} {(p + q)² - (p - q)²}

= (p² + 2pq + q² + p² - 2pq + q²) (p² + 2pq + q² - p² + 2pq - q²)

= 2 (p² + q²) (4pq)

= 8pq (p² + q²)

= R.H.S. (Proved)