簡約 (3x+2y)^2*(5x+3y)^2

解

簡約

(3 x + 2 y)^{2} \cdot (5 x + 3 y)^{2}

(3 x + 2 y)^{2} (5 x + 3 y)^{2}

解答ステップ

(3 x + 2 y)^{2} (5 x + 3 y)^{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

(3 x + 2 y)^{2} (5 x + 3 y)^{2} = ((3 x + 2 y) (5 x + 3 y))^{2}

= ((3 x + 2 y) (5 x + 3 y))^{2}

指数の規則を適用する:

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

= (3 x + 2 y)^{2} (5 x + 3 y)^{2}