簡約 (a+b-c)^2(a-b+c)^2

解

簡約

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

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

解答ステップ

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

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m},

, 以下を想定

a \geq 0, b \geq 0

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

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

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

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