中科新闻网hes管理:初一数学题
来源：百度文库 编辑：中科新闻网 时间：2024/05/09 07:36:55
因式分解:
X^4+X^2+1
64(m+n)^2-9(m-n)^2
X^4+X^2+1
64(m+n)^2-9(m-n)^2
X^4+X^2+1
=X^4+2X^2+1
=(X^2+1)^2-X^2
=(X^2+1+X)(X^2+1-X)
64(m+n)^2-9(m-n)^2
=[8(m+n)]^2-[3(m-n)]^2
=[8(m+n)+3(m-n)][8(m+n)-3(m-n)]
=(11m+5n)(5m+11n)
64(m+n)^2-9(m-n)^2=(11m+5n)(5m+11n)
X^4+X^2+1=(x^2-x+1)(x^2+x+1)
x^4+x^2+1=x^4+2x^2+1-x^2
=(x^2+1)^2-x^2
=(x^2+x+1)*(x^2-x+1)
X^4+X^2+1
=[x^2-1][x^4+x^2+1]/[x^2-1]
=[x^6-1]/[x^2-1]
=[x^3-1][x^3+1]/[x+1][x-1]
=[x-1][x^2+x+1][x^3+1]/[x+1][x-1]
=[x^2+x+1][x^3+1]/[x+1]
64(m+n)^2-9(m-n)^2
=[8(m+n)+3(m-n)][8(m+n)-3(m-n)]
=[11m+5n][5m+11n]