Question

If $P$ be the sum of odd term and $Q$ that of even terms in the expansion of $(x+a{)}^n$ , then the value of $\left[\right(x+a{)}^{2n}-(x-a{)}^{2n}]$ equals

• A. $PQ$
• B. $2PQ$
• C. $4$$PQ$
• D. None of these

Answer 1

The correct option is C $4$$PQ$

$P=\frac{(x+a{)}^n+(x-a{)}^n}{2}$ ...(i)
$Q=\frac{(x+a{)}^n-(x-a{)}^n}{2}$ ...(ii)
Hence, $2P.2Q$
$=4PQ$
$=\left[\right(x+a{)}^n+(x-a{)}^n]\left[\right(x+a{)}^n-(x-a{)}^n]$
$=(x+a{)}^{2n}-(x-a{)}^{2n}$