$\text{ If the sum of odd terms and the sum of even terms in the expansion of }(\mathrm{x}+\mathrm{a}{)}^{\mathrm{n}}$

$\text{ are }\mathrm{p}\text{ and }\mathrm{q}\text{ respectively then }{\mathrm{p}}^2+{\mathrm{q}}^2=$

• A

  ${\left({\text{x}}^{\text{2}}{\text{+a}}^{\text{2}}\right)}^{\text{n}}$

• B

  ${\left({\text{x}}^{\text{2}}{\text{-a}}^{\text{2}}\right)}^{\text{n}}$

• C

  $\frac{1}{2}\left[{\left(\text{x+a}\right)}^{\text{2n}}+{\left(\text{x-a}\right)}^{\text{2n}}\right]$

• D

  $\frac{1}{2}\left[{\left(\text{x+a}\right)}^{\text{2n}}-{\left(\text{x-a}\right)}^{\text{2n}}\right]$