Solve -3/2(-3/2a^{2}b^{3})(-3/2a^{3}b^{2})+(-4/3a^{5}b^{4})(-frac{4}{3}a^{2}b^{2})-frac{16}{9}(-a^{3}b^{2})(-a^4b^4)+frac{27}{8}a^5b^5

$$- \frac { 3 } { 2 } ( - \frac { 3 } { 2 } a ^ { 2 } b ^ { 3 } ) ( - \frac { 3 } { 2 } a ^ { 3 } b ^ { 2 } ) + ( - \frac { 4 } { 3 } a ^ { 5 } b ^ { 4 } ) ( - \frac { 4 } { 3 } a ^ { 2 } b ^ { 2 } ) - \frac { 16 } { 9 } ( - a ^ { 3 } b ^ { 2 } ) ( - a ^ { 4 } b ^ { 4 } ) + \frac { 27 } { 8 } a ^ { 5 } b ^ { 5 }$$

Evaluate

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Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-\frac{3}{2}\left(-\frac{3}{2}\right)a^{5}b^{3}\left(-\frac{3}{2}\right)b^{2}-\frac{4}{3}a^{5}b^{4}\left(-\frac{4}{3}\right)a^{2}b^{2}-\frac{16}{9}\left(-a^{3}\right)b^{2}\left(-a^{4}\right)b^{4}+\frac{27}{8}a^{5}b^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-\frac{3}{2}\left(-\frac{3}{2}\right)a^{5}b^{5}\left(-\frac{3}{2}\right)-\frac{4}{3}a^{5}b^{4}\left(-\frac{4}{3}\right)a^{2}b^{2}-\frac{16}{9}\left(-a^{3}\right)b^{2}\left(-a^{4}\right)b^{4}+\frac{27}{8}a^{5}b^{5}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$-\frac{3}{2}\left(-\frac{3}{2}\right)a^{5}b^{5}\left(-\frac{3}{2}\right)-\frac{4}{3}a^{7}b^{4}\left(-\frac{4}{3}\right)b^{2}-\frac{16}{9}\left(-a^{3}\right)b^{2}\left(-a^{4}\right)b^{4}+\frac{27}{8}a^{5}b^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-\frac{3}{2}\left(-\frac{3}{2}\right)a^{5}b^{5}\left(-\frac{3}{2}\right)-\frac{4}{3}a^{7}b^{6}\left(-\frac{4}{3}\right)-\frac{16}{9}\left(-a^{3}\right)b^{2}\left(-a^{4}\right)b^{4}+\frac{27}{8}a^{5}b^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-\frac{3}{2}\left(-\frac{3}{2}\right)a^{5}b^{5}\left(-\frac{3}{2}\right)-\frac{4}{3}a^{7}b^{6}\left(-\frac{4}{3}\right)-\frac{16}{9}\left(-a^{3}\right)b^{6}\left(-a^{4}\right)+\frac{27}{8}a^{5}b^{5}$$

Multiply -\frac{3}{2} and -\frac{3}{2} to get \frac{9}{4}.

$$\frac{9}{4}a^{5}b^{5}\left(-\frac{3}{2}\right)-\frac{4}{3}a^{7}b^{6}\left(-\frac{4}{3}\right)-\frac{16}{9}\left(-a^{3}\right)b^{6}\left(-a^{4}\right)+\frac{27}{8}a^{5}b^{5}$$

Multiply \frac{9}{4} and -\frac{3}{2} to get -\frac{27}{8}.

$$-\frac{27}{8}a^{5}b^{5}-\frac{4}{3}a^{7}b^{6}\left(-\frac{4}{3}\right)-\frac{16}{9}\left(-a^{3}\right)b^{6}\left(-a^{4}\right)+\frac{27}{8}a^{5}b^{5}$$

Multiply -\frac{4}{3} and -\frac{4}{3} to get \frac{16}{9}.

$$-\frac{27}{8}a^{5}b^{5}+\frac{16}{9}a^{7}b^{6}-\frac{16}{9}\left(-a^{3}\right)b^{6}\left(-a^{4}\right)+\frac{27}{8}a^{5}b^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-\frac{27}{8}a^{5}b^{5}+\frac{16}{9}a^{7}b^{6}-\frac{16}{9}\left(-1\right)a^{7}b^{6}\left(-1\right)+\frac{27}{8}a^{5}b^{5}$$

Multiply -\frac{16}{9} and -1 to get \frac{16}{9}.

$$-\frac{27}{8}a^{5}b^{5}+\frac{16}{9}a^{7}b^{6}+\frac{16}{9}a^{7}b^{6}\left(-1\right)+\frac{27}{8}a^{5}b^{5}$$

Multiply \frac{16}{9} and -1 to get -\frac{16}{9}.

$$-\frac{27}{8}a^{5}b^{5}+\frac{16}{9}a^{7}b^{6}-\frac{16}{9}a^{7}b^{6}+\frac{27}{8}a^{5}b^{5}$$

Combine \frac{16}{9}a^{7}b^{6} and -\frac{16}{9}a^{7}b^{6} to get 0.

$$-\frac{27}{8}a^{5}b^{5}+\frac{27}{8}a^{5}b^{5}$$

Combine -\frac{27}{8}a^{5}b^{5} and \frac{27}{8}a^{5}b^{5} to get 0.

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Factor

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Solution Steps

Factor out \frac{1}{72}.

$$\frac{-243a^{2}b^{3}a^{3}b^{2}+128a^{5}b^{4}a^{2}b^{2}-128a^{3}b^{2}a^{4}b^{4}+243a^{5}b^{5}}{72}$$

Consider -243a^{5}b^{5}+128a^{7}b^{6}-128a^{7}b^{6}+243a^{5}b^{5}. Factor out a^{5}b^{5}.

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