(x+2y)^4-3(x^2-4y^2)^4-18(2y-x)^4

(x+2y)^4-3(x^2-4y^2)^4-18(2y-x)^4
(x+2y)^4-3(x^2-4y^2)^4-18(2y-x)^4

(x+2y)^4-3(x^2-4y^2)^4-18(2y-x)^4
题目错了：第二个括号的指数是2,不是4
原式=[(x+2y)²]²-3(x+2y)²*(x-2y)²-18[(x-2y)²]²
=[(x+2y)²-6(x-2y)²][(x+2y)²+3(x-2y)²]
=(x²+4xy+4y²-6x²+24xy-24y²)(x²+4xy+4y²+3x²-12xy+12y²)
=(-5x²+28xy--20y²)(4x²-8xy+16y²)
=-4(5x²-28xy+20y²)(x²-2xy+4y²)

令 a = (x+2y)², b = (x-2y)²
(x+2y)^4 - 3(x²-4y²)² - 18(2y-x)^4
= (x+2y)^4 - 3[(x+2y)(x-2y)]² - 18(x-2y)^4
= a² - 3ab -18b²
= (a -6b)(a + 3b)
...

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令 a = (x+2y)², b = (x-2y)²
(x+2y)^4 - 3(x²-4y²)² - 18(2y-x)^4
= (x+2y)^4 - 3[(x+2y)(x-2y)]² - 18(x-2y)^4
= a² - 3ab -18b²
= (a -6b)(a + 3b)
= [(x+2y)² - 6(x-2y)²][(x+2y)² + 3(x-2y)²]

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