(1)8x^3+4x^2-2x-1 (2)4a^2-20ab+25b^2-36 (3)4xy+1-4x^2-y^2 (4)a^4b+a^3b^2_a^2b^3-ab^4 (5)x^6-y^6-2x^3+1 (6)x^2(x+1)-y(xy+x)都是分解因式的题目 要写具体过程

Question

(1)8x^3+4x^2-2x-1 (2)4a^2-20ab+25b^2-36 (3)4xy+1-4x^2-y^2 (4)a^4b+a^3b^2_a^2b^3-ab^4 (5)x^6-y^6-2x^3+1 (6)x^2(x+1)-y(xy+x)
都是分解因式的题目 要写具体过程

Answer 1

应该是因式分解吧
1.
8x^3+4x^2-2x-1
=(8x^3+4x^2) - (2x+1)
=(4x^2-1)(2x+1)
=(2x-1) * (2x+1)^2
2.
4a^2-20ab+25b^2-36
=(4a^2-20ab+25b^2) - 36
=(2a-5b)^2 - 36
=(2a-5b-6)(2a-5b+6)
3.
4xy+1-4x^2-y^2
=1 - (4x^2 + 4xy - y^2)
=1 - (2x-y)^2
=(1-2x+y)(1+2x-y)
4.
a^4b+a^3b^2_a^2b^3-ab^4
=(a^4b+a^3b^2) - (a^2b^3+ab^4)
=a^3b(a + b) - ab^3(a+b)
=(a^3b - ab^3)(a+b)
=ab(a^2 - b^2)(a+b)
=ab(a-b)(a+b)^2
5.
x^6-y^6-2x^3+1
=(x^6-2x^3+1)-y^6
=(x^3 - 1)^2 - y^6
=(x^3-1-y^3)(x^3-1+y^3)
6.
x^2(x+1)-y(xy+x)
=x^3 + x^2 - xy^2 - xy
=(x^3 - xy^2) + (x^2 - xy)
=x(x^2 - y^2) + x(x-y)
=x(x-y)(x+y) + x(x-y)
=x(x-y)(x+y+1)
我没去检查,也许会有一两处错误,不过我想你应该会了
就是提取公因式