因式分解(^代表几次方,） ①x^3+6x+1+6 ②2x^4-x^3-6x^2-x+2 ③(x-y)^2-3(x-y)

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因式分解(^代表几次方,） ①x^3+6x+1+6 ②2x^4-x^3-6x^2-x+2 ③(x-y)^2-3(x-y)-10 ④4a^2-b^2+4a-2b
⑤x^2-2xy+y^2-2x+2y-3
⑥x^5+x+1
⑦(x+y-2xy)(x+y-2)+(xy-1)^2
⑧x^2-y^2-2x-4y-3
⑨7x^2-19x-6
⑩x^3+(2a+1)x^2+(a^2+2a-1)x+a^2-1
x是唉可思不要理解成乘号了
重要的是过程

①x^3+6x+1+6
②2x^4-x^3-6x^2-x+2
=x²(2x+3)(x-2)-(x-2)
=(x-2)(2x³+3x²-1)
=(x-2)[2x²(x+1)+(x+1)(x-1)]
=(x-2)(x+1)(2x²+x-1)
=(x-2)(x+1)²(2x-1)
③(x-y)^2-3(x-y)-10
=（x-y-5)(x-y+3)
④4a^2-b^2+4a-2b
=(2a+b)(2a-b)+2(2a-b)
=(2a-b)(2a+b+2)
⑤x^2-2xy+y^2-2x+2y-3
=(x-y)²-2(x-y)-3
=(x-y-3)(x-y+1)
⑥x^5+x+1
⑦(x+y-2xy)(x+y-2)+(xy-1)^2
=(x+y)²-2xy(x+y)+4xy-2(x+y)+x²y²-2xy+1
=(x+y)²-2(x+y)(xy+1)+(xy+1)²
=(x+y-xy-1)²
=(x-1)²(1-y)²
⑧x^2-y^2-2x-4y-3
=(x+y)(x-y)-2x-4y-3
=(x+y+1)(x-y-3)
⑨7x^2-19x-6
=(7x+2)(x-3)
⑩x^3+(2a+1)x^2+(a^2+2a-1)x+a^2-1
=x³+1+(2a+1)x²+(2a+1)x+(a²-2)x+(a²-2)
=(x+1)(x²-x+1)+(2a+1)x(x+1)+(a²-2)(x+1)
=(x+1)(x²+2ax+a²-1)
=(x+1)(x+a+1)(x+a-1)

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