Question

数学八年级上册 因式分解题目求解，，求过程

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

Answer 1

解 -16m²+(m-n)²
=(m-n)²-16m²
=(m-n)²-(4m)²
=[(m-n)+4m][(m-n)-4m]
=(5m-n)(-3m-n)

(x-2y)²-4(2x-y)²
=(x-2y)²-[2(2x-y)]²
=[(x-2y)+2(2x-y)][(x-2y)-2(2x-y)]
=(x-2y+4x-2y)(x-2y-4x+2y)
=-3x(5x-4y)

(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)]
=2(a+c)×2(b+d)
=4(a+c)(b+d)

m²n²-9p²
=(mn)²-(3p)²
=(mn+3p)(mn-3p)

(a+m)²-(a-n)²
=[(a+m)+(a-n)][(a+m)-(a-n)]
=(2a+m-n)(m+n)

16(x+y)²-25(x-y)²
=[4(x+y)]²-[5(x-y)]²
=[4(x+y)+5(x-y)][4(x+y)-5(x-y)]
=(4x+4y+5x-5y)(4x+4y-5x+5y)
=(9x-y)(-x+9y)

16a^4-b^4 ^表示乘方
=(4a²)-(b²)²
=(4a²+b²)(4a²-b²)
=(4a²+b²)(2a+b)(2a-b)

a²(m-n)+b²(n-m)
=a²(m-n)-b²(m-n)
=(m-n)(a²-b²)
=(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)²-[5(a-4)]²﹜
=3[(a+1)+5(a-4)][(a+1)-5(a-4)]
=3(a+1+5a-20)(a+1-5a+20)
=3(6a-19)(-4a+21)

a^(2n+1)-16a^(2n-1)
=[a^(2n-1)]×(a²-16)
=[a^(2n-1)]×(a+4)(a-4)

9(a-b)²-25(a+b)²
=[3(a-b)]²-[5(a+b)]²
=[3(a-b)+5(a+b)][3(a-b)-5(a+b)]
=(3a-3b+5a+5b)(3a-3b-5a-5b)
=(8a+2b)(-2a-8b)
=-4(4a+b)(a+4b)

Answer 2

（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)