Mathematics
Senior High
(2)で最後なぜこうなるのか、輪環順にしたとき符号が変えられるのか、教えてください。
練習 14 次の式を因数分解せよ。
(1) ab(a-b)+bc(b-c)+ca(c-a)
(2) a(b²-c²)+b(c² - a²)+c(a²-6²))-(-2
(1) ab(a-b)+bc(b-c)+ca(c-a)
=
= (b-c)a² - (b² - c²)a+bc(b-c)
= (b-c)a² - (b+c)(b-c)a+bc(b-c)
= (b-c){a² - (b+c)a+bc}
= (b-c)(a - b)(ac) = -(a - b)(b-c)(c-a)
(2) a(b²-c²)+b(c² - a²)+c(a² - b²)
= (c-b)a² + (b²-c²)a + (bc²-b2c)
= (c-b)a²+(b+c)(b-c)a+bc(c-b)
= (c-b)a² - (b+c)(c-b)a+bc(c-b)
= (c-b){a² - (b+c)a+bc}
= (c-b)(a - b)(a–c)
=(a-b)(b-c)(c-a) なぜ変える?
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