Question

帮忙算这些因式分解的题目 8x^3y^3-1/125 4a^2+b^2+c^2-4ab+4ac-2bc 5X^2-15x+2xy-6y a^2(x+y)^3-a^2b^3

还有几个 帮帮忙
7(a+b)^2-5(a+b)-2

6x^2-7x-3

x^3+2x^2+2x+1

2X^2-3x-1

x^2+4x-1

Answer 1

8x^3y^3-1/125
=(2xy)^3-(1/5)^3
=(2xy-1/5)(4x^2y^2+2xy/5+1/25)
4a^2+b^2+c^2-4ab+4ac-2bc
=(2a-b)^2+2c(2a-b)+c^2
=(2a-b+c)^2
( 5X^2-15x+2xy-6y
=x(5x+2y)-3(5x+2y)
=(5x+2y)(x-3)
a^2(x+y)^3-a^2b^3
=a^2[(x+y)^3-b^3]
=a^2(x+y-b)[(x+y)^2+b(x+y)+b^2]
=a^2(x+y-b)(x^2+2xy+y^2+bx+by+b^2)
希望能帮到你，祝学习进步O(∩_∩)O

追问

还有几个 帮帮忙
7(a+b)^2-5(a+b)-2

6x^2-7x-3

x^3+2x^2+2x+1

2X^2-3x-1

x^2+4x-1

16-8xy-16x^2-y^2

追答

7(a+b)^2-5(a+b)-2=[7(a+b)+2][(a+b)-1]=(7a+7b+2)(a+b-1)
6x^2-7x-3=(3x+1)(2x-3)
x^3+2x^2+2x+1=(x^3+x^2)+(x^2+2x+1)=x^2(x+1)+(x+1)^2=(x+1)(x^2+x+1)
2X^2-3x-1 (在有理数范围内不能分解因式)
=2(x^2-3x/2-1/2)=2(x^2-3x/2+9/16-17/16)
=2[(x-3/4)^2-(√17/4)^2]=2(x-3/4+√17/4)(x-3/4-√17/4)
x^2+4x-1 (在有理数范围内不能分解因式)
=x^2+4x+4-5
=(x+2)^2-(√5)^2
=(x+2+√5)(x+2-√5)
16-8xy-16x^2-y^2
=16-(16x^2+8xy+y^2)
=4^2-(4x+y)^2
=(4+4x+y)(4-4x-y)
希望能帮到你，祝学习进步O(∩_∩)O

Answer 2

8x^3y^3-1/125
=(2xy-1/5)(4x^2y^2+2/5xy+1/25)
4a^2+b^2+c^2-4ab+4ac-2bc
=4a^2-4a(b+c)+(b+c)^2
=(2a-b-c)^2
5X^2-15x+2xy-6y
=5x(x-3)+2y(x-3)
=(5x+2y)(x-3)
a^2(x+y)^3-a^2b^3
=a^2((x+y)^3-b^3)
=a^2(x+y-b)((x+y)^2+(x+y)b+b^2)

Answer 3

7(a+b)^2-5(a+b)-2
=[（a+b)-1]*[7(a+b)+2]

6x^2-7x-3
=(3x+1)(2x-3)

x^3+2x^2+2x+1
=(x^3+1)+(2x^2+2x)
=(x+1)(x^2-x-1)+2x(x+1)
=(x+1)(x^2+x-1)

2X^2-3x-1
=???

x^2+4x-1
=？？？？

追问

后面两个干嘛不写上