高専の数学解説

第1章 1.14

(1)

x2−y2+2y−1=x2−(y−1)2=(x−y+1)(x+y−1)x^2 - y^2 + 2y - 1 = x^2 - (y-1)^2 = (x-y+1)(x+y-1)

(2)

x2−y2−4x−2y+3=(x−2)2−(y+1)2=(x+y−1)(x−y−3)x^2 - y^2 - 4x - 2y + 3 = (x-2)^2 - (y+1)^2 = (x+y-1)(x-y-3)

(3)

x4+x2−2=(x2+2)(x2−1)=(x2+2)(x−1)(x+1)x^4 + x^2 - 2 = (x^2+2)(x^2-1) = (x^2+2)(x-1)(x+1)

(4)

a4−10a2+9=(a2−9)(a2−1)=(a−3)(a+3)(a−1)(a+1)a^4 - 10a^2 + 9 = (a^2-9)(a^2-1) = (a-3)(a+3)(a-1)(a+1)

(5)

(a+b)2−(a−b)2=a2+2ab+b2−a2+2ab−b2=4ab(a+b)^2 - (a-b)^2 = a^2 + 2ab + b^2 - a^2 + 2ab - b^2 = 4ab

(6)

(a2+b2)2−4a2b2=a4+2a2b2+b4−4a2b2=a4−2a2b2+b4=(a2−b2)2=(a+b)2(a−b)2(a^2+b^2)^2 - 4a^2b^2 = a^4 + 2a^2b^2 + b^4 - 4a^2b^2 = a^4 - 2a^2b^2 + b^4 = (a^2-b^2)^2 = (a+b)^2(a-b)^2

解説: r31bn1z