prove : (p+q)²-(p-q)² = 8pq (p²+q²)
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Step-by-step explanation:
Given,(p+q)^4 -(p-q)^4=8pq(p^2+q^2).
LHS=(p+q)^4 -(p-q)^4
Substitute the above formule in LHS.
=p^4 + 4p^3q +6p^2 q^2 +4pq^3+q^4 -[p^4 - 4p^3 q +6 p^2q^2 -4pq^3 +q^4]
=8p^3q+8pq^3
=8pq[p^2 + q^2]
=RHS.
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