因式分解5道题,越多越好,随便回答几道
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/07/08 02:44:28
因式分解5道题,越多越好,随便回答几道
1) ( 2x^n-1 ) - ( 4x^2n-2 )
2) x(x-y)(3x+y) - 2x(x+y)(x-y)
3) 3 (a + b ) ^2 - 27c^2
4) (5m^2 +3n^2)^2 - (3m^2 + 5n^2)^2
5) x^4 - 18x^2 +81
做好后想确定一下,回答的越多越好,
1) ( 2x^n-1 ) - ( 4x^2n-2 )
2) x(x-y)(3x+y) - 2x(x+y)(x-y)
3) 3 (a + b ) ^2 - 27c^2
4) (5m^2 +3n^2)^2 - (3m^2 + 5n^2)^2
5) x^4 - 18x^2 +81
做好后想确定一下,回答的越多越好,
![因式分解5道题,越多越好,随便回答几道](/uploads/image/z/14868159-15-9.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A35%E9%81%93%E9%A2%98%2C%E8%B6%8A%E5%A4%9A%E8%B6%8A%E5%A5%BD%2C%E9%9A%8F%E4%BE%BF%E5%9B%9E%E7%AD%94%E5%87%A0%E9%81%93)
1) ( 2x^n-1 ) - ( 4x^2n-2 )
=2X^n-1(1-X^n-1)
2) x(x-y)(3x+y) - 2x(x+y)(x-y)
=X(X-Y)[3X+y-2x-2y]
=X(X-Y)(x-y)
3) 3 (a + b ) ^2 - 27c^2
=3[(a+b)^2-9c^2]
=3(a+b+3c)(a+b-3c)
4) (5m^2 +3n^2)^2 - (3m^2 + 5n^2)^2
=[5m^2+3n^2+3m^2+5n^2][5m^2+3n^2-3m^2-5n^2]
=16(m^2+n^2)(m^2-n^2)
=16(m^2+n^2)(m+n)(m-n)
5) x^4 - 18x^2 +81
=(X^2-9)^2
=(X+3)^2(X-3)^2.
=2X^n-1(1-X^n-1)
2) x(x-y)(3x+y) - 2x(x+y)(x-y)
=X(X-Y)[3X+y-2x-2y]
=X(X-Y)(x-y)
3) 3 (a + b ) ^2 - 27c^2
=3[(a+b)^2-9c^2]
=3(a+b+3c)(a+b-3c)
4) (5m^2 +3n^2)^2 - (3m^2 + 5n^2)^2
=[5m^2+3n^2+3m^2+5n^2][5m^2+3n^2-3m^2-5n^2]
=16(m^2+n^2)(m^2-n^2)
=16(m^2+n^2)(m+n)(m-n)
5) x^4 - 18x^2 +81
=(X^2-9)^2
=(X+3)^2(X-3)^2.