What is (1/3 x^2-3)^2 ?

The solution to (1/3 x^2-3)^2 is (x^4)/9-2x^2+9

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simplify (1/3 x^2-3)^2

simplify

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

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

Solution steps

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

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

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

Apply Perfect Square Formula:

(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}

Simplify

(\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

3 lo g_{4} (3) - lo g_{4} (12) + 2

2 (\frac{1}{2} x^{2} + 8)^{2} - 8

\frac{21}{60}

x^{4} - 10 x^{2} y^{2} + 25 y^{4}

\frac{1}{3 + 2}