-2x^6+32x^2

=-2x^2(x^4-16)
=-2x^2(x^2+4)(x^2-4)
-2x^2(x^2+4)(x+2)(x-2)

-2x^6+32x^2
=-2x^2(x^4-16)
=-2x^2[(x^2)^2-4^2]
=-2x^2(x^2+4)(x^2-4)

这题先提公因式-2x^2,接着再套书上的公式a^2-b^2=(a+b)(a-b)

原式=2(16x^2-x^6)
=2(4x-x^3)(4x+x^3)
=2x^2(4-x^2)(4+x^2)
=2x^2(2-x)(2+x)(4+x^2)