Question

因式分解：2ax-10ay+5by-bx 计算：已知a-b=5,b-c=3,求a＾2+b＾2+c＾2-ab-ac-bc的

Answer 1

2ax-10ay+5by-bx

＝2a(x-5y)-b(x-5y)

＝（2a-b)(x-5y)

由a-b=5,b-c=3得a-c=8

又(a-b)^2=a^2=b^2-2ab

(a-c)^2=a^2=c^2-2ac

(c-b)^2=c^2=b^2-2bc

等式两边分别相加,

得(a-b)^2+(a-c)^2+(c-b)^2=2a^2+2b^2+2c^2-2ab-2ac-2bc

a^2+b^2+c^2-ab-ac-bc=(25+9+64)/2=49