1.计算:(2x-5y)²(5x+2y)² 2.因式分解：(x²-2x)²-11(x²-2x)-24
问题描述：
1.计算:(2x-5y)²(5x+2y)² 2.因式分解：(x²-2x)²-11(x²-2x)-24
答
(1)100X4+241X2Y2-420X3Y-420XY3+100Y4
(2)(X-3)(X+1)(X-4)(X+2)-48
答
1.(2X-5Y)²（5X+2Y）²=（4X²-25Y²）（25X²+4Y²）=100X²+16X²Y²-625X²Y²-600Y²=100X²-609X²Y²-600Y²
2.X四次方-4X²-11X²+22X-24=X四次方-15X²+22X-24
答
.(2X-5Y)²（5X+2Y）².
=[ (2X-5Y)（5X+2Y）]²
=（10X² - 21XY + 10Y²）²
=100x^4 -420yx^3+641X²Y²-420xy^3+100y^4
（x^2+2x）^2-11(x^2+2x)+24
令x^2+2x=t
原式=t^2-11t+24
=t^2-(8+3)t+8*3
=(t-3)(t-8)
=(x^2+2x-3)(x^2+2x-8)
=[x^2+(3+(-1))x+3*(-1)][x^2+(4+(-2))x+4*(-2)]
=(x-1)(x+3)(x-2)(x+4)