展開する a(a-1)x^2+(2a^2-1)x+a(a+1)

解

展開する

a (a - 1) x^{2} + (2 a^{2} - 1) x + a (a + 1)

a^{2} x^{2} - a x^{2} + 2 x a^{2} - x + a^{2} + a

解答ステップ

a (a - 1) x^{2} + (2 a^{2} - 1) x + a (a + 1)

= a x^{2} (a - 1) + x (2 a^{2} - 1) + a (a + 1)

拡張

a x^{2} (a - 1) : a^{2} x^{2} - a x^{2}

= a^{2} x^{2} - a x^{2} + x (2 a^{2} - 1) + a (a + 1)

拡張

x (2 a^{2} - 1) : 2 x a^{2} - x

= a^{2} x^{2} - a x^{2} + 2 x a^{2} - x + a (a + 1)

拡張

a (a + 1) : a^{2} + a

= a^{2} x^{2} - a x^{2} + 2 x a^{2} - x + a^{2} + a