Solve (5/3a+1/4b)*(3/5a-1/2b)-a^2+frac{2}{3}a^2+frac{1}{4}b^2=

$$( \frac { 5 } { 3 } a + \frac { 1 } { 4 } b ) \cdot ( \frac { 3 } { 5 } a - \frac { 1 } { 2 } b ) - a ^ { 2 } + \frac { 2 } { 3 } a ^ { 2 } + \frac { 1 } { 4 } b ^ { 2 } =$$

Evaluate

$$-\frac{41ab}{60}+\frac{2a^{2}}{3}+\frac{b^{2}}{8}$$

Solution Steps

Use the distributive property to multiply \frac{5}{3}a+\frac{1}{4}b by \frac{3}{5}a-\frac{1}{2}b and combine like terms.

$$a^{2}-\frac{41}{60}ab-\frac{1}{8}b^{2}-a^{2}+\frac{2}{3}a^{2}+\frac{1}{4}b^{2}$$

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

$$-\frac{41}{60}ab-\frac{1}{8}b^{2}+\frac{2}{3}a^{2}+\frac{1}{4}b^{2}$$

Combine -\frac{1}{8}b^{2} and \frac{1}{4}b^{2} to get \frac{1}{8}b^{2}.

$$-\frac{41}{60}ab+\frac{1}{8}b^{2}+\frac{2}{3}a^{2}$$

Expand

$$-\frac{41ab}{60}+\frac{2a^{2}}{3}+\frac{b^{2}}{8}$$

Solution Steps

Use the distributive property to multiply \frac{5}{3}a+\frac{1}{4}b by \frac{3}{5}a-\frac{1}{2}b and combine like terms.

$$a^{2}-\frac{41}{60}ab-\frac{1}{8}b^{2}-a^{2}+\frac{2}{3}a^{2}+\frac{1}{4}b^{2}$$

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

$$-\frac{41}{60}ab-\frac{1}{8}b^{2}+\frac{2}{3}a^{2}+\frac{1}{4}b^{2}$$

Combine -\frac{1}{8}b^{2} and \frac{1}{4}b^{2} to get \frac{1}{8}b^{2}.

$$-\frac{41}{60}ab+\frac{1}{8}b^{2}+\frac{2}{3}a^{2}$$