Question

因式分解题目 求大神回答 越快分越多

x的四次方+x³+x²-1
4（x+y）²+5-20（x+y-1)
x²-y²-z²-2yz
9x的五次方-72x²y³
········

Answer 1

解
x^4+x³+x²-1
=x³(x+1)+(x²-1)
=x³(x+1)+(x-1)(x+1)
=(x+1)(x³+x-1)

4(x+y)²+5-20(x+y-1)
=4(x+y)²-20(x+y)+25
=[2(x+y)]²-2×2(x+y)×5+5²
=[2(x+y)-5]²
=(2x+2y-5)²

x²-y²-z²-2yz
=x²-(y²+z²+2yz)
=x²-(y+z)²
=[x-(y+z)][x+(y+z)]
=(x-y-z)(x+y+z)

9x^5-72x²y³
=9x²(x³-8y³)
=9x²[x³-(2y)³]————利用立方差公式
=9x²(x-2y)(x²+2xy+4y²)
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