Question

приведите к стандартному виду:(1+х+х^2+х^3)^2
(1-x+x^2-x^3+x^4)^2

Answer 1

$(1+x+ x^{2} + x^{3} ) ^{2} = ((1+x)+x^2(1+x))^{2} = ((1+x)(1+ x^{2} ))^{2} = \\ \\= (1+x)^2*(1+x^2)^2=(1+2x+x^2)*(1+2x^2+x^4)= \\ \\ =1+2x^2+x^4+2x+4x^3+2x^5+x^2+2x^4+x^6= \\ \\ =x^6+2x^5+3x^4+4x^3+3x^2+1$