${{\left( 1+x \right)}^{4}}+{{\left( 1-x \right)}^{4}}=C_{4}^{0}{{1}^{4}}+C_{4}^{1}{{1}^{3}}.x+C_{4}^{2}{{1}^{2}}.{{x}^{2}}+C_{4}^{3}{{1}}.{{x}^{3}}+C_{4}^{4}{{x}^{4}}$
$=1+4x+6{{x}^{2}}+4{{x}^{3}}+{{x}^{4}}$
${{\left( 1+x \right)}^{4}}+{{\left( 1-x \right)}^{4}}=C_{4}^{0}{{1}^{4}}+C_{4}^{1}{{1}^{3}}.x+C_{4}^{2}{{1}^{2}}.{{x}^{2}}+C_{4}^{3}{{1}}.{{x}^{3}}+C_{4}^{4}{{x}^{4}}$
$=1+4x+6{{x}^{2}}+4{{x}^{3}}+{{x}^{4}}$