Question

初二上册数学 因式分解

Answer 1

解(1) a²-9b²
=a²-(3b)²
=(a+3b)(a-3b)

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

解(3) (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)

解(4) a²(x-y)-b²(x-y)
=(x-y)(a²-b²)
=(x-y)(a+b)(a-b)

解(5) 16m^4-n^4 ^表示乘方
=(4m²)-(n²)²
=(4m²+n²)(4m²-n²)
=(4m²+n²)(2m+n)(2m-n)

解(6) (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)]
=(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)