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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