Question

数学-因式分解 详细过程,急急急急！！！！速度可再加财富

1.x²-y²=20,求[(x-y)²+4xy]{(x+y)²-4xy]的值。

2.3a^4-2/3a²+1/27

3.2(x²-3y²)²+24x²y²

Answer 1

1.x²-y²=20,
[(x-y)²+4xy]{(x+y)²-4xy]
=[x²-2xy+y²+4xy][x²+2xy+y²-4xy]
=[x²+2xy+y²][x²-2xy+y²]
=(x+y)²(x-y)²
=((x+y)(x-y))²
=(x²-y²)²
=20²
=400
2.3a^4-2/3a²+1/27
=1/27(81a^4-18a²+1)
=1/27(9a^2-1)^2
=1/27(3a+1)^2(3a-1)^2
3.2(x²-3y²)²+24x²y²
=2((x²-3y²)²+12x²y²)
=2(x^4-6x²y²+9y²+12x²y²)
=2(x^4+6x²y²+9y²)
=2(x²+3y²)²