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

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

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

simplify

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

\frac{4 x ^{2} y ^{2}}{3}

Solution steps

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

Expand

(\frac{1}{2} x^{2} + \frac{2}{3} y^{2})^{2} : \frac{9 x ^{4} + 24 x ^{2} y ^{2} + 16 y ^{4}}{36}

= \frac{9 x ^{4} + 24 x ^{2} y ^{2} + 16 y ^{4}}{36} - (\frac{1}{2} x^{2} - \frac{2}{3} y^{2})^{2}

Expand

- (\frac{1}{2} x^{2} - \frac{2}{3} y^{2})^{2} : - \frac{9 x ^{4} - 24 x ^{2} y ^{2} + 16 y ^{4}}{36}

= \frac{9 x ^{4} + 24 x ^{2} y ^{2} + 16 y ^{4}}{36} - \frac{9 x ^{4} - 24 x ^{2} y ^{2} + 16 y ^{4}}{36}

Join

\frac{9 x ^{4} + 24 x ^{2} y ^{2} + 16 y ^{4}}{36} - \frac{9 x ^{4} - 24 x ^{2} y ^{2} + 16 y ^{4}}{36} : \frac{4 x ^{2} y ^{2}}{3}

= \frac{4 x ^{2} y ^{2}}{3}

3 x + 2 y 0.5 z - 9 p

- 9 w - (- 1.6 x + 10)

\frac{3 x _{5}}{3}

(3 a^{2} b - 5 a^{3} b^{2})^{3}

4 + 625 y^{8}

What is (1/2*x^2+2/3*y^2)^2-(1/2*x^2-2/3*y^2)^2 ?
The solution to (1/2*x^2+2/3*y^2)^2-(1/2*x^2-2/3*y^2)^2 is (4x^2y^2)/3