展開する (ax^2+bx+c)^2

解

展開する

(a x^{2} + b x + c)^{2}

a^{2} x^{4} + b^{2} x^{2} + 2 a x^{3} b + 2 a x^{2} c + 2 b c x + c^{2}

解答ステップ

(a x^{2} + b x + c)^{2}

指数の規則を適用する:

a^{b + c} = a^{b} \cdot a^{c}

(a x^{2} + b x + c)^{2} = (a x^{2} + b x + c) (a x^{2} + b x + c)

= (a x^{2} + b x + c) (a x^{2} + b x + c)

括弧を分配する

= a x^{2} a x^{2} + a x^{2} b x + a x^{2} c + b x a x^{2} + b x b x + b x c + c a x^{2} + c b x + cc

簡素化

a x^{2} a x^{2} + a x^{2} b x + a x^{2} c + b x a x^{2} + b x b x + b x c + c a x^{2} + c b x + cc : a^{2} x^{4} + b^{2} x^{2} + 2 a x^{3} b + 2 a x^{2} c + 2 b c x + c^{2}

= a^{2} x^{4} + b^{2} x^{2} + 2 a x^{3} b + 2 a x^{2} c + 2 b c x + c^{2}