计算下列分解因式:(2a+b)(2a-3b)-3a(2a+b) x(x+y)(x-y)-x(x+y)2次方

法1 (2a+b)(2a-3b)-3a(2a+b) =2a(2a-3b)+b(2a-3b)-6a²-3ab
=4a²-6ab+2ab-3b²-6a²-3ab=-2a²-7ab-3b²=-(2a+b)(a+3b)
x(x+y)(x-y)-x(x+y)²=x(x²-y²)-x(x²+2xy+y²）=x³-xy²-x³-2x²y-xy² =-2xy²-2x²y=-2xy(x+y)
>.< 用到完全平方公式，平方差公式，十字相乘法 ，大众题型解法，分解因式都可采用
法2 (2a+b)(2a-3b)-3a(2a+b)=(2a+b)[(2a-3b)-3a]=(2a+b)(-a-3b)
x(x+y)(x-y)-x(x+y)²= x(x+y)[(x-y)-(x+y)] = -2xy(x+y)
>.<提取公因式，对于这题此法更简单

(2a+b)(2a-3b)-3a(2a+b)
解：原式= (4a^2-6ab+2ab-3b^2)-6a^2-3ab
= -2a^2-7ab-3b^2
= - (2a^2+7ab+3b^2)
= - (2a+b)(a+3b)
x(x+y)(x-y)-x(x+y)^2
=x(x+y)[(x-y)-(x+y)](合并同类项)
=x(x+y)*2y
=2xy(x+y)

解：原式=(2a+b)【(2a-3b)-3a】=(2a+b)(-a-3b)
x(x+y)(x-y)-x(x+y)^2=x(x+y)[(x-y)-(x+y)]=-xy(x+y)

(2a+b)(2a-3b)-3a(2a+b)
= (4a^2-6ab+2ab-3b^2)-6a^2-3ab
= -2a^2-7ab-3b^2
= - (2a^2+7ab+3b^2)
= - (2a+b)(a+3b)
x(x+y)(x-y)-x(x+y)^2
= x(x+y)[(x-y)-(x+y)]
= -xy(x+y)

次方用的汉字表示的 2次方用的二 3次方用的三
（1）=2a×2a+2a×(-3b)+b×2a+b×(-3b)-3a×2a-3a×b
=4a二-6ab+2ab-3b二-6a二-3ab
= -2a二-3b二-7ab
= -(a+3b)(2a+b)

（2）=(x二+xy)(x-y)-x(x二+2xy+y二)
=x二×x+x二×(-y)+xy×x+xy×(-y)-x×x二-x×2xy-x×y二
=x三-x二y+x二y-xy二-x三-xy二-2x二y
= -2xy二-2x二y
= -2xy(y+x)

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