簡約 (1/3 x^2-3)^2

解

簡約

(\frac{1}{3} x^{2} - 3)^{2}

\frac{x ^{4}}{9} - 2 x^{2} + 9

解答ステップ

(\frac{1}{3} x^{2} - 3)^{2}

\frac{1}{3} x^{2} = \frac{x ^{2}}{3}

= (\frac{x ^{2}}{3} - 3)^{2}

完全平方式を適用する:

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

a = \frac{x ^{2}}{3}, b = 3

= (\frac{x ^{2}}{3})^{2} - 2 \cdot \frac{x ^{2}}{3} \cdot 3 + 3^{2}

簡素化

(\frac{x ^{2}}{3})^{2} - 2 \cdot \frac{x ^{2}}{3} \cdot 3 + 3^{2} : \frac{x ^{4}}{9} - 2 x^{2} + 9

= \frac{x ^{4}}{9} - 2 x^{2} + 9