# Is there an easy way to simplify $(P+Q)^2 - (P-Q)^2$ where $P$ and $Q$ are matrices?

P and Q are different matrices that are 2x2. I have tried to do this by letting both equal a 'made-up' matrix with pro numerals, but the expansion process is very long. Is there an easy way to simplify this?

• It is $2PQ+2QP$ – Kavi Rama Murthy Aug 13 at 8:57

$$(P+Q)^2=(P+Q)(P+Q) = P\cdot P + P\cdot Q + Q\cdot P + Q\cdot Q$$