作业帮因式分解：1.4a方-20ab+25b方-36
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/16 19:29:43
因式分解：1.4a方-20ab+25b方-36
2.x四次方+64
3.x三次方+5x-6
4.2a方b方-7ab+6
5.2xy-x方-y方+1
6.（a+b)(a-b)+c(2b-c)
2.x四次方+64
3.x三次方+5x-6
4.2a方b方-7ab+6
5.2xy-x方-y方+1
6.（a+b)(a-b)+c(2b-c)
1.4a方-20ab+25b方-36
4a^2 - 20ab + 25b^2 - 36
=(2a - 5b)^2 - 6^2
=(2a - 5b + 6)(2a - 5b - 6)
2.x四次方+64
x^4+64
=x^4+16x^2+64-16x^2
=(x^2+8)-(4x)^2
=(x^2-4x+8)(x^2+4x+8)
3.x三次方+5x-6
x^3+5x-6
=x^3-x+6x-6
=x(x^2 - 1)+6(x-1)
=x(x+1)(x-1)+6(x-1)
=(x-1)[x(x+1)+6]
=(x-1)(x^2+x+6)
4.2a方b方-7ab+6
=(2ab-3)(ab-2)
5.2xy-x方-y方+1
2xy-x^2-y^2+1
=1-(x^2-2xy+y^2)
=1-(x-y)^2
=(1-x+y)(1+x-y)
6.（a+b)(a-b)+c(2b-c)
=a^2-b^2+2bc-c^2
=a^2-(b^2-2bc+c^2)
=a^2-(b-c)^2
=(a-b+c)(a+b-c)
4a^2 - 20ab + 25b^2 - 36
=(2a - 5b)^2 - 6^2
=(2a - 5b + 6)(2a - 5b - 6)
2.x四次方+64
x^4+64
=x^4+16x^2+64-16x^2
=(x^2+8)-(4x)^2
=(x^2-4x+8)(x^2+4x+8)
3.x三次方+5x-6
x^3+5x-6
=x^3-x+6x-6
=x(x^2 - 1)+6(x-1)
=x(x+1)(x-1)+6(x-1)
=(x-1)[x(x+1)+6]
=(x-1)(x^2+x+6)
4.2a方b方-7ab+6
=(2ab-3)(ab-2)
5.2xy-x方-y方+1
2xy-x^2-y^2+1
=1-(x^2-2xy+y^2)
=1-(x-y)^2
=(1-x+y)(1+x-y)
6.（a+b)(a-b)+c(2b-c)
=a^2-b^2+2bc-c^2
=a^2-(b^2-2bc+c^2)
=a^2-(b-c)^2
=(a-b+c)(a+b-c)