# Coefficient coefficient

If a binomial expansion is given by $(1+x)^{10} = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots + a_{10} x^{10}.$

then find the value of the expression $(a_0 - a_2 + a_4 - a_6 +a_8 - a_{10} )^2 + (a_1 - a_3 + a_5 - a_7 + a_9 )^2.$

×