Solve (-3ab+2ab)^{2}-(3/2ab)(-4/3ab)+(-2a^{2}b^{3})^{2}-(-2a)^3(-3/2a)(-b^2)^3-3(-ab)^2

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\left(-3ab+2ab\right)^{2}-\frac{3}{2}a^{2}b\left(-\frac{4}{3}\right)b+\left(-2a^{2}b^{3}\right)^{2}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Multiply a and a to get a^{2}.

\left(-3ab+2ab\right)^{2}-\frac{3}{2}a^{2}b^{2}\left(-\frac{4}{3}\right)+\left(-2a^{2}b^{3}\right)^{2}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Multiply b and b to get b^{2}.

\left(-ab\right)^{2}-\frac{3}{2}a^{2}b^{2}\left(-\frac{4}{3}\right)+\left(-2a^{2}b^{3}\right)^{2}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Combine -3ab and 2ab to get -ab.

\left(-1\right)^{2}a^{2}b^{2}-\frac{3}{2}a^{2}b^{2}\left(-\frac{4}{3}\right)+\left(-2a^{2}b^{3}\right)^{2}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Expand \left(-ab\right)^{2}.

1a^{2}b^{2}-\frac{3}{2}a^{2}b^{2}\left(-\frac{4}{3}\right)+\left(-2a^{2}b^{3}\right)^{2}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Calculate -1 to the power of 2 and get 1.

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

Multiply \frac{3}{2} and -\frac{4}{3} to get -2.

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

The opposite of -2a^{2}b^{2} is 2a^{2}b^{2}.

3a^{2}b^{2}+\left(-2a^{2}b^{3}\right)^{2}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Combine 1a^{2}b^{2} and 2a^{2}b^{2} to get 3a^{2}b^{2}.

3a^{2}b^{2}+\left(-2\right)^{2}\left(a^{2}\right)^{2}\left(b^{3}\right)^{2}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Expand \left(-2a^{2}b^{3}\right)^{2}.

3a^{2}b^{2}+\left(-2\right)^{2}a^{4}\left(b^{3}\right)^{2}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

3a^{2}b^{2}+\left(-2\right)^{2}a^{4}b^{6}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

3a^{2}b^{2}+4a^{4}b^{6}-\left(-2a\right)^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Calculate -2 to the power of 2 and get 4.

3a^{2}b^{2}+4a^{4}b^{6}-\left(-2\right)^{3}a^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Expand \left(-2a\right)^{3}.

3a^{2}b^{2}+4a^{4}b^{6}-\left(-8a^{3}\left(-\frac{3}{2}\right)a\left(-b^{2}\right)^{3}\right)-3\left(\left(-a\right)b\right)^{2}

Calculate -2 to the power of 3 and get -8.

3a^{2}b^{2}+4a^{4}b^{6}-12a^{3}a\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

Multiply -8 and -\frac{3}{2} to get 12.

3a^{2}b^{2}+4a^{4}b^{6}-12a^{4}\left(-b^{2}\right)^{3}-3\left(\left(-a\right)b\right)^{2}

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

3a^{2}b^{2}+4a^{4}b^{6}-12a^{4}\left(-b^{2}\right)^{3}-3\left(-a\right)^{2}b^{2}

Expand \left(\left(-a\right)b\right)^{2}.

3a^{2}b^{2}+4a^{4}b^{6}-12a^{4}\left(-b^{2}\right)^{3}-3a^{2}b^{2}

Calculate -a to the power of 2 and get a^{2}.

3a^{2}b^{2}+4a^{4}b^{6}-12a^{4}\left(-1\right)^{3}\left(b^{2}\right)^{3}-3a^{2}b^{2}

Expand \left(-b^{2}\right)^{3}.

3a^{2}b^{2}+4a^{4}b^{6}-12a^{4}\left(-1\right)^{3}b^{6}-3a^{2}b^{2}

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

3a^{2}b^{2}+4a^{4}b^{6}-12a^{4}\left(-1\right)b^{6}-3a^{2}b^{2}

Calculate -1 to the power of 3 and get -1.

3a^{2}b^{2}+4a^{4}b^{6}+12a^{4}b^{6}-3a^{2}b^{2}

Multiply -12 and -1 to get 12.

3a^{2}b^{2}+16a^{4}b^{6}-3a^{2}b^{2}

Combine 4a^{4}b^{6} and 12a^{4}b^{6} to get 16a^{4}b^{6}.

16a^{4}b^{6}

Combine 3a^{2}b^{2} and -3a^{2}b^{2} to get 0.