Question

分解因式，拜托了。

1-12x^2y^2+48x^4y^4-64x^6y^6

Answer 1

由立方差公式可以知道，
1-64x^6y^6
=1 -(4x^2y^2)^3
=(1-4x^2y^2)(1+4x^2y^2 +16x^4y^4)
由平方差公式可以知道，
-12x^2y^2+48x^4y^4
= -12x^2y^2(1 -4x^2y^2)

所以
1-12x^2y^2+48x^4y^4-64x^6y^6
=(1-4x^2y^2)(1+4x^2y^2 +16x^4y^4) -12x^2y^2(1 -4x^2y^2)
=(1-4x^2y^2) (1+4x^2y^2 +16x^4y^4 - 12x^2y^2)
=(1-4x^2y^2) (1-8x^2y^2+16x^4y^4)
=(1-4x^2y^2)^3
=(1-2xy)^3 (1+2xy)^3

Answer 2

原式=-(64x^6y^6-1)+48x^4y^4-12x²y²
=-(4x²y²-1)(16x^4y^4+4x²y²+1)+12x²y²(4x²y²-1)
=-(4x²y²-1)(16x^4y^4+4x²y²+1-12x²y²)
=-(4x²y²-1)(16x^4y^4-8x²y²+1)
=-(4x²y²-1)(4x²y²-1)²
=-(2xy+1)³(2xy-1)³

Answer 3

0