Question

Представьте многочлен 8m ^6 + 36m^4 n^2 + 54m^2 n^4 + 27n^6 в виде куба двучлена. Отметьте верный ответ. (2m + 3n^2)^3(4m^2 + 3n^2)^3 (2m^2 + 3n)^3 (2m^2 + 3n^2)^3

Answer 1

$\displaystyle 8m^6+36m^4n^2+54m^2n^4+27n^6=2^3m^3^*^2+3*4m^4*3n^2+3*2m^2*9n^4+3^3n^3^*^2=\\ \\ 2^3(m^2)^3+3*2^2m^2^*^2*3n^2+3*2m^2*3^2n^2^*^2+3^3(n^2)^3=\\ \\ (2m^2)^3+3*2^2(m^2)^2*3n^2+3*2m^2*3^2(n^2)^2+(3n^2)^3=\\ \\ (2m^2)^3+3(2m^2)^2*3n^2+3*2m^2(3n^2)^2+(3n^2)^3=(2m^2+3n^2)^3$