What is (1/3*a^2-3/2*b^2)^2 ?

The solution to (1/3*a^2-3/2*b^2)^2 is (a^4)/9-a^2b^2+(9b^4)/4

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simplify (1/3a^2-3/2b^2)^2

simplify

(\frac{1}{3} \cdot a^{2} - \frac{3}{2} \cdot b^{2})^{2}

\frac{a ^{4}}{9} - a^{2} b^{2} + \frac{9 b ^{4}}{4}

Solution steps

(\frac{1}{3} a^{2} - \frac{3}{2} b^{2})^{2}

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

\frac{3}{2} b^{2} = \frac{3 b ^{2}}{2}

= (\frac{a ^{2}}{3} - \frac{3 b ^{2}}{2})^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= \frac{a ^{4}}{9} - a^{2} b^{2} + \frac{9 b ^{4}}{4}

\frac{( 9 x 1 0 ^{9} \cdot 2 x 1 0 ^{- 5} )}{0. 4 ^{2}}

(x^{6})^{3} (x^{2})

- 6 x^{0}

(x^{2})^{- 3} \cdot 2 x^{3}

3 sin (x) - sin^{2} (x)

What is (1/3*a^2-3/2*b^2)^2 ?
The solution to (1/3*a^2-3/2*b^2)^2 is (a^4)/9-a^2b^2+(9b^4)/4