Question

高一 数学 因式分解（要有详细过程） 请详细解答,谢谢! (14 20:52:48)

1.       3x2+5xy--2y2+x+9y--4
2.       (x2+x+1)(x2+x+2)--12
3.       (a+b--2ab)(a+b--2)+(1--ab)2
 

Answer 1

1.
由于3x2+5xy-2y2=(3x-y)(x+2y)，
故可设
3x2+5xy-2y2+x+9y-4
=(3x-y+a)(x+2y+b)
=3x2+5xy-2y2+(a+3b)x+(2a-b)y+ab.

由于3x2+5xy-2y2=(3x-y)(x+2y)，
故纳稿闷可设
3x2+5xy-2y2+x+9y-4
=(3x-y+a)(x+2y+b)
=3x2+5xy-2y2+(a+3b)x+(2a-b)y+ab.

比较两边系数洞弯最后解得a=4 b=1
∴原式=(3x-y+4)(x+2y-1).

2.
令a=x^2+x+1
则敬缓x^2+x+2=a+1

（x^2+x+1)(x^2+x+2)-12
=a(a+1)-12
=a^2+a-12
=(a+4)(a-3)
=(x^2+x+5)(x^2+x-2)
=(x^2+x+5)(x+2)(x-1)

3.(a+b-2ab)(a+b-2)+(1-ab)(1-ab)
=[(a+b)-2ab][(a+b)-2]+(1-ab)(1-ab)
=(a+b)^2-2(ab+1)(a+b)+4ab+(1-ab)^2
=(a+b)^2-2(ab+1)(a+b)+[4ab+(1-ab)^2]
=(a+b)^2-2(ab+1)(a+b)+(1+ab)^2
=[(a+b)-(ab+1)]^2
=[(a-1)(1-b)]^2
=(a-1)^2*(b-1)^2

Answer 2

1. 3x²+5xy--2y²+x+9y--4
=(3x-y)(x+2y)-(3x-y)+4x+8y-4
=(3x-y)(x+2y-1)+4(x+2y-1)
=(3x-y+4)(x+2y-1)

2. (x²+x+1)(x²+x+2)--12
=(x²漏段则+x)²+3(x²+x)+2-12
=(x²+x)²返棚+3(x²+x)-10
=(x²燃岩+x+5)(x²+x-2)
=(x²+x+5)(x+2)(x-1)

3. (a+b--2ab)(a+b--2)+(1--ab)²
=(a+b)²-(2+2ab)(a+b)+4ab+1-2ab+a²b²
=(a+b)²-(2+2ab)(a+b)+1+2ab+a²b²
=(a+b)²-(2+2ab)(a+b)+(1+ab)²
=[(1+ab)-(a+b)]²
=(ab-a-b+1)²
=[a(b-1)-(b-1)]²
=(a-1)²(b-1)²

Answer 3

任意选择

Answer 4

3x^2+5xy-2y^2+x+9y-4
=(3x-y)(x+2y)+x+9y-4
=(3x-y+4)(x+2y-1)

(x^2+x+1)(x^2+x+2)-12
=(x^2+x+1)^2+(x^2+x+1)-12
=(x^2+x+1-3)(x^2+x+1+4)
=(x^2+x-2)(x^2+x+5)
=(x+2)(x-1)(x^2+x+5)

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