Question

因式分解 ab(c^2 -d^2)+cd(a^2 -b^2)和x^5 +x+1

Answer 1

ab(c^2 -d^2)+cd(a^2 -b^2)

=abc^2+a^2cd-abd^2-b^2cd

=ac(bc+ad)-bd(ad+bc)

=(ac-bd)(ad+bc)

x^5+x+1

=x^5-x^2+x^2+x+1

=x^2(x^3-1)+(x^2+x+1)

=x^2(x-1)(x^2+x+1)+(x^2+x+1)

=(x^3-x^2)(x^2+x+1)+(x^2+x+1)

=(x^3-x^2+1)(x^2+x+1)