Question

把下列格式分解因式，要过程，十万火急

﹙¹﹚X²﹙X-Y﹚²﹣4﹙Y-X﹚²
﹙2﹚16﹙X+Y﹚²﹣25﹙X-Y﹚²
﹙3﹚3﹙A+B﹚²-27C
﹙4﹚M²﹙P-Q﹚﹣P+Q

Answer 1

﹙¹﹚X²﹙X-Y﹚²﹣4﹙Y-X﹚²
=x²(x-y)²-4(x-y)²
=(x-y)²(x²-4)
=(x-y)²(x+2)(x-2)

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

﹙3﹚3﹙A+B﹚²-27C ²
=3[(a+b)²-9]
=3(a++3)(a+b-3)

﹙4﹚M²﹙P-Q﹚﹣P+Q
=m²(p-q)-(p-q)
=(p-q)(m²-1)
=(p-q)(m+1)(m-1)

追问

能再算一题吗？

追答

=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/10)(1+1/10)
=1/2× 3/2×2/3 × 4/3×3/4 ×……×9/10 ×11/10
=1/2×11/10
=11/20