Solve 4/3(a^2-5)+5/7{-3/5[-4(2a-3)+8a^2]}

$$\frac { 4 } { 3 } ( a ^ { 2 } - 5 ) + \frac { 5 } { 7 } \{ - \frac { 3 } { 5 } [ - 4 ( 2 a - 3 ) + 8 a ^ { 2 } ] \}$$

Evaluate

$$-\frac{44a^{2}}{21}+\frac{24a}{7}-\frac{248}{21}$$

Solution Steps

Use the distributive property to multiply \frac{4}{3} by a^{2}-5.

$$\frac{4}{3}a^{2}-\frac{20}{3}+\frac{5}{7}\left(-\frac{3}{5}\right)\left(-4\left(2a-3\right)+8a^{2}\right)$$

Multiply \frac{5}{7} and -\frac{3}{5} to get -\frac{3}{7}.

$$\frac{4}{3}a^{2}-\frac{20}{3}-\frac{3}{7}\left(-4\left(2a-3\right)+8a^{2}\right)$$

Use the distributive property to multiply -4 by 2a-3.

$$\frac{4}{3}a^{2}-\frac{20}{3}-\frac{3}{7}\left(-8a+12+8a^{2}\right)$$

Use the distributive property to multiply -\frac{3}{7} by -8a+12+8a^{2}.

$$\frac{4}{3}a^{2}-\frac{20}{3}+\frac{24}{7}a-\frac{36}{7}-\frac{24}{7}a^{2}$$

Subtract \frac{36}{7} from -\frac{20}{3} to get -\frac{248}{21}.

$$\frac{4}{3}a^{2}-\frac{248}{21}+\frac{24}{7}a-\frac{24}{7}a^{2}$$

Combine \frac{4}{3}a^{2} and -\frac{24}{7}a^{2} to get -\frac{44}{21}a^{2}.

$$-\frac{44}{21}a^{2}-\frac{248}{21}+\frac{24}{7}a$$

Expand

$$-\frac{44a^{2}}{21}+\frac{24a}{7}-\frac{248}{21}$$

Solution Steps

Use the distributive property to multiply \frac{4}{3} by a^{2}-5.

$$\frac{4}{3}a^{2}-\frac{20}{3}+\frac{5}{7}\left(-\frac{3}{5}\right)\left(-4\left(2a-3\right)+8a^{2}\right)$$

Multiply \frac{5}{7} and -\frac{3}{5} to get -\frac{3}{7}.

$$\frac{4}{3}a^{2}-\frac{20}{3}-\frac{3}{7}\left(-4\left(2a-3\right)+8a^{2}\right)$$

Use the distributive property to multiply -4 by 2a-3.

$$\frac{4}{3}a^{2}-\frac{20}{3}-\frac{3}{7}\left(-8a+12+8a^{2}\right)$$

Use the distributive property to multiply -\frac{3}{7} by -8a+12+8a^{2}.

$$\frac{4}{3}a^{2}-\frac{20}{3}+\frac{24}{7}a-\frac{36}{7}-\frac{24}{7}a^{2}$$

Subtract \frac{36}{7} from -\frac{20}{3} to get -\frac{248}{21}.

$$\frac{4}{3}a^{2}-\frac{248}{21}+\frac{24}{7}a-\frac{24}{7}a^{2}$$

Combine \frac{4}{3}a^{2} and -\frac{24}{7}a^{2} to get -\frac{44}{21}a^{2}.

$$-\frac{44}{21}a^{2}-\frac{248}{21}+\frac{24}{7}a$$