To know Everyone Know Identities - 3?

Algebra Level 2

True or False :

( p − q ) 3 = p 3 + q 3 − 3 p q ( p − q ) \color{#BA33D6}{( p - q )^ 3 = p^3 + q^3 - 3pq ( p - q )}

True False I don't know this Identity.

Anish Harsha by Anish Harsha , 20, India

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1 solution

not a clear explanation, but there are a few options. First, give values to p and q (whatever value you want) then start calculating. the statement will result in being false then, we could try calculating them without giving values (p-q)^2 = p^2 + q^2 - 2pq(p-q) but that won't apply to (p-q)^3 because it would result in [p^2 + q^2 - 2pq(p-q)] (p-q) which won't give p^3 + q^3 - epq(p-q) sorry for the non clear explanation, but since there are no solutions... guess my chaotic thinking has to do it for now xD

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Moderator note:

Yes, checking specific values of p , q p,q could tell us if an identity is untrue.

A clearer explanation would be to expand out all of the terms completely, and then compare them.

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