作业帮因式分解：X³+9X²+26X+24,bc(b+c)+ca(c-a)-ab(a+b),8x³
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/11/09 00:02:22
因式分解：X³+9X²+26X+24,bc(b+c)+ca(c-a)-ab(a+b),8x³-(x-y)³-(x+y)³
X³+9X²+26X+24
=(X³+7X²+12X)+(2X²+14X+24)
=X(X²+7X+12)+2(X²+7X+12)
=(X+2)(X²+7X+12)
=(X+2)(X+3)(X+4)
bc(b+c)+ca(c-a)-ab(a+b)
=c[b(b+c)+a(c-a)]-ab(a+b)
=c(b²+bc+ac-a²)-ab(a+b)
=c[(bc+ac)+(b²-a²)]-ab(a+b)
=c[c(b+a)+(b+a)(b-a)]-ab(a+b)
=c(a+b)(c+b-a)-ab(a+b)
=(a+b)(c²+bc-ac-ab)
=(a+b)(b+c)(c-a)
8x³-(x-y)³-(x+y)³
=8x³-[(x-y)³+(x+y)³]
=8x³-[(x-y)+(x+y)]*[(x-y)²+(x+y)²-(x-y)(x+y)]
=8x³-2x*[2x²+2y²-(x²-y²)]
=8x³-2x(x²+3y²)
=8x³-2x³-6xy²
=6x³-6xy²
=6x(x²-y²)
=6x(x-y)(x+y)
=(X³+7X²+12X)+(2X²+14X+24)
=X(X²+7X+12)+2(X²+7X+12)
=(X+2)(X²+7X+12)
=(X+2)(X+3)(X+4)
bc(b+c)+ca(c-a)-ab(a+b)
=c[b(b+c)+a(c-a)]-ab(a+b)
=c(b²+bc+ac-a²)-ab(a+b)
=c[(bc+ac)+(b²-a²)]-ab(a+b)
=c[c(b+a)+(b+a)(b-a)]-ab(a+b)
=c(a+b)(c+b-a)-ab(a+b)
=(a+b)(c²+bc-ac-ab)
=(a+b)(b+c)(c-a)
8x³-(x-y)³-(x+y)³
=8x³-[(x-y)³+(x+y)³]
=8x³-[(x-y)+(x+y)]*[(x-y)²+(x+y)²-(x-y)(x+y)]
=8x³-2x*[2x²+2y²-(x²-y²)]
=8x³-2x(x²+3y²)
=8x³-2x³-6xy²
=6x³-6xy²
=6x(x²-y²)
=6x(x-y)(x+y)
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