解答

✨ 最佳解答 ✨

参考・概略です

 多いので、式だけです

(6) (x+y-z)(x-y+z)
 ={x+(y-z)}{x-(y-z)}
 =x²-(y-z)²「
 =x²-{y²-2yz+z²}
 =x²-y²+2yz-z²

(7) (x⁴+1)(x²+1)(x+1)(x-1)
 =(x⁴+1)(x²+1){(x+1)(x-1)}
 =(x⁴+1)(x²+1)(x²-1²)
 =(x⁴+1){(x²+1)(x²-1)}
 =(x⁴+1){(x²)²-(1)²}
 =(x⁴+1)(x⁴-1)
 ={(x⁴)²-(1)²}
 =x⁸-1

(8) (x-1)(x+1)(x-2)(x+2)
 ={(x-1)(x+1)}{(x-2)(x+2)}
 ={x²-1}{x²-4}
 =(x²)²-5(x²)+4
 =x⁴-5x²+4

(9) (x+4)(x+2)(x-1)(x-3)
 ={(x+4)(x-3)}{(x+2)(x-1)}
 ={x²+x-12}{x²+x-2}
 ={(x²+x)-12}{(x²+x)-2}
 =(x²+x)²-14(x²+x)+24
 =x⁴+2x³+x²-14x²-14x+24
 =x⁴+2x³-13x²-14x+24

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