高専の数学解説

第1章 1.28

(1)

(x2−3x+2)(2x−1)=2x3−x2−6x2+3x+4x−2=2x3−7x2+7x−2(x^2-3x+2)(2x-1)=2x^3-x^2-6x^2+3x+4x-2=2x^3-7x^2+7x-2

(2)

(x+2)(x2−2x+4)=x3+2x2−2x2−4x+4x+8=x3+8(x+2)(x^2-2x+4)=x^3+2x^2-2x^2-4x+4x+8=x^3+8

(3)

(1−a−a2)(3−2a)=3−2a−3a+2a2−3a2+2a3=3−5a−a2+2a3(1-a-a^2)(3-2a)=3-2a-3a+2a^2-3a^2+2a^3=3-5a-a^2+2a^3

(4)

(x2−y2)(x4−x2y2+y4)=x6−x4y2+x2y4−x4y2+x2y4−y6=x6−2x4y2+2x2y4−y6(x^2-y^2)(x^4-x^2y^2+y^4)=x^6-x^4y^2+x^2y^4-x^4y^2+x^2y^4-y^6=x^6-2x^4y^2+2x^2y^4-y^6

(5)

(x2−1)(x3−2x2+1)=x5−2x4+x2−x3+2x2−1=x5−2x4−x3+3x2−1(x^2-1)(x^3-2x^2+1)=x^5-2x^4+x^2-x^3+2x^2-1=x^5-2x^4-x^3+3x^2-1

(6)

(x+y+z)(x2+y2+z2−xy−yz−zx)(x+y+z)(x^2+y^2+z^2-xy-yz-zx)

=x3+xy2+xz2−x2y−xyz−x2z+x2y+y3+yz2−xy2−y2z−xyz+x2z+y2z+z3−xyz−yz2−xz2=x^3+xy^2+xz^2-x^2y-xyz-x^2z+x^2y+y^3+yz^2-xy^2-y^2z-xyz+x^2z+y^2z+z^3-xyz-yz^2-xz^2

=x3+y3+z3−3xyz=x^3+y^3+z^3-3xyz

解説: r31bn1z