Question

因式分解题目、急急急！

1.（x-y）^2+2(x-y)+1=
2.(x^2-6x)^2-81=
3.x^4-8a^2x^2+16a^4=
4.(a-b)^3-4ab(b-a)=
5.2-128a^6=
6.(x-1)^2(3x-2)+(2-3x)
7.1/2x^4-2y^2=
8.x^2(x-4)+y^2(4-x)=

Answer 1

1.（x-y）^2+2(x-y)+1=
=(x-y+1)^2

2.(x^2-6x)^2-81=
=(x^2-6x+9)(x^2-6x-9)
=(x-3)^2(x^2-6x-9)

3.x^4-8a^2x^2+16a^4=
=(x^2-4)^2
=(x+2)^2(x-2)^2

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

5.2-128a^6
=2(1-64a^6)
=2(1+8a^3)(1-8a^3)
=2(1+2a)(1-2a+4a^2)(1-2a)(1+2a+4a^2)

6.(x-1)^2(3x-2)+(2-3x)
=(x-1)^2(3x-2)-(3x-2)
=(3x-2)[(x-1)^2-1]
=(3x-2)(x-1+1)(x-1-1)
=x(3x-2)(x-2)

7.1/2x^4-2y^2
=1/2(x^4-4y^2)
=1/2(x^2+2y)(x^2-2y)

8.x^2(x-4)+y^2(4-x)
=x^2(x-4)-y^2(x-4)
=(x-4)(x^2-y^2)
=(x-4)(x+y)(x-y)

Answer 2

1.（x-y）^2+2(x-y)+1
=(x-y+1)^2

2.(x^2-6x)^2-81
=(x^2-6x+9)(x^2-6x-9)
=(x-3)^2(x^2-6x-9)

3.x^4-8a^2x^2+16a^4
=(x^2-4a^2)^2
=(x+2a)^2(x-2a)^2

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

5.2-128a^6
=2(1-64a^6)
=2(1+8a^3)(1-8a^3)
=2(1+2a)(1-2a+4a^2)(1-2a)(1+2a+4a^2)

6.(x-1)^2(3x-2)+(2-3x)
=(3x-2)[(x-1)^2-1]
=(3x-2)(x-1+1)(x-1-1)
=x(3x-2)(x-2)

7.1/2x^4-2y^2
=1/2*(x^4-4y^2)
=1/2*(x^2+2y)(x^2-2y)

8.x^2(x-4)+y^2(4-x)
=(x-4)(x^2-y^2)
=(x-4)(x+y)(x-y)

Answer 3

1 (x-y+1)^2
2 (x^-6x-9)(x-3)^2
3 (x^2-4a^2)^2=(x-2a)^2(x+2a)^2
4 (a-b)((a-b)^2+4ab)=(a-b)(a+b)^2
5 2(1-8a^3)^2=2(1-2a)(1+4a+a^2)
6 (3x-2)((x-1)^2-1)=(3x-2)(x-2)x
7 2((1/2x)^2-y^2)=2(1/2x-y)(1/2x+y)
8 (x-4)(x^2-y^2)=(x-4)(x-y)(x+y)

Answer 4

1.(x-y+1)^2
2.(x-3)^2(x^2-6x-9)
3.(x+2a)^2(x-2a)^2
4.(a-b)(a^2+5ab+b^2)
5.2(1-2a)(1+2a)(1+32a^4)

Answer 5

dfgd

Answer 6

1.（x-y）^2+2(x-y)+1=[(x-y)+1]^2
=(x-y+1)^2
2.(x^2-6x)^2-81=[(x^2-6x)+9][(x^2-6x)-9]
=(x^2-6x+9)(x^2-6x-9)
=(x-3)^2 *(x^2-6x-9)
3.x^4-8a^2x^2+16a^4=(x^2-4a^2)^2
=[(x-2a)(x+2a)]^2
=(x-2a)^2(x+2a)^2
4.(a-b)^3-4ab(b-a)=(a-b)[(a-b)^2+4ab]
=(a-b)(a^2+2ab+b^2)
=(a-b)(a+b)^2
5.2-128a^6=2(1-64a^6)=2(1-8a^3)(1+8a^3)
=2(1-2a)(1+2a+4a^2)(1+2a)(1-2a+4a^2)
=2(1-2a)(1+2a)(1+2a+4a^2)(1-2a+4a^2)

6.(x-1)^2(3x-2)+(2-3x)=(3x-2)[(x-1)^2-1]
=(3x-2)(x-1+1)(x-1-1)
=x(3x-2)()x-2)
7.1/2x^4-2y^2=1/2(x^2-4y^2)
=1/2(x-2y)(x+2y)
8.x^2(x-4)+y^2(4-x)= (x-4)(x^2-y^2)
=(x-4)(x-y)(x+y)