因式分解(1)-16m²+(m-n)² (2)(x-2y)²-4(2x-y)²
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/09/13 04:25:25
因式分解(1)-16m²+(m-n)² (2)(x-2y)²-4(2x-y)² (3)(a+b+c+d)²-(a-b+c-d)² (4)m²n²-9p² (5)(a+m)²-(a-n)² (6)16(x+y)²-25(x-y)² 还有几道
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(1)-16m²+(m-n)²
=(m-n)²-16m²
=(m-n+4m)(m-n-4m)
=(5m-n)(-3m-n)
=-(5m-n)(3m+n)
(2)(x-2y)²-4(2x-y)²
=((x-2y)+2(2x-y))((x-2y)-2(2x-y))
=(5x-4y)(-3x)
=-3x(5x-4y)
(3)(a+b+c+d)²-(a-b+c-d)²
=(a+b+c+d+a-b+c-d)(a+b+c+d-a+b-c+d)
=(2a+2c)(2b+2d)
=4(a+c)(b+d)
(4)m²n²-9p²
=(mn+3p)(mn-3p)
(5)(a+m)²-(a-n)²
=(a+m+a-n)(a+m-a+n)
=(2a+m-n)(m+n)
(6)16(x+y)²-25(x-y)²
=(4(x+y)+5(x-y))(4(x+y)-5(x-y))
=(9x-y)(-x+9y)
16a^4-b^4
=(4a^2+b^2)(4a^2-b^2)
=(4a^2+b^2)(2a+b)(2a-b)
a^2(m-n)+b^2(n-m)
=a^2(m-n)-b^2(m-n)
=(m-n)(a^2-b^2)
=(m-n)(a+b)(a-b)
3(a+1)^2-75(a-4)^2
=3((a+1)^2-25(a-4)^2)
=3((a+1+5(a-4))((a+1-5(a-4))
=3(6a-19)(-4a+21)
a^2n+1-16a^2n-1
=a^2n-1(a^2-16)
=a^2n-1(a+4)(a-4)
9(a-b)^2-25(a+b)^2
=(3(a-b)+5(a+b))(3(a-b)-5(a+b))
=(8a+2b)(-2a-8b)
=-(8a+2b)(2a+8b)
=(m-n)²-16m²
=(m-n+4m)(m-n-4m)
=(5m-n)(-3m-n)
=-(5m-n)(3m+n)
(2)(x-2y)²-4(2x-y)²
=((x-2y)+2(2x-y))((x-2y)-2(2x-y))
=(5x-4y)(-3x)
=-3x(5x-4y)
(3)(a+b+c+d)²-(a-b+c-d)²
=(a+b+c+d+a-b+c-d)(a+b+c+d-a+b-c+d)
=(2a+2c)(2b+2d)
=4(a+c)(b+d)
(4)m²n²-9p²
=(mn+3p)(mn-3p)
(5)(a+m)²-(a-n)²
=(a+m+a-n)(a+m-a+n)
=(2a+m-n)(m+n)
(6)16(x+y)²-25(x-y)²
=(4(x+y)+5(x-y))(4(x+y)-5(x-y))
=(9x-y)(-x+9y)
16a^4-b^4
=(4a^2+b^2)(4a^2-b^2)
=(4a^2+b^2)(2a+b)(2a-b)
a^2(m-n)+b^2(n-m)
=a^2(m-n)-b^2(m-n)
=(m-n)(a^2-b^2)
=(m-n)(a+b)(a-b)
3(a+1)^2-75(a-4)^2
=3((a+1)^2-25(a-4)^2)
=3((a+1+5(a-4))((a+1-5(a-4))
=3(6a-19)(-4a+21)
a^2n+1-16a^2n-1
=a^2n-1(a^2-16)
=a^2n-1(a+4)(a-4)
9(a-b)^2-25(a+b)^2
=(3(a-b)+5(a+b))(3(a-b)-5(a+b))
=(8a+2b)(-2a-8b)
=-(8a+2b)(2a+8b)
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