Solve -left(8{m}^frac{5{2}}+5n^3right)left(8{m}^frac{5{2}}-5n^3right)

$$- \left( 8 { m }^{ \frac{ 5 }{ 2 } } +5 { n }^{ 3 } \right) \left( 8 { m }^{ \frac{ 5 }{ 2 } } -5 { n }^{ 3 } \right)$$

Evaluate

$$25n^{6}-64m^{5}$$

Solution Steps

To find the opposite of 8m^{\frac{5}{2}}+5n^{3}, find the opposite of each term.

$$\left(-8m^{\frac{5}{2}}-5n^{3}\right)\left(8m^{\frac{5}{2}}-5n^{3}\right)$$

Use the distributive property to multiply -8m^{\frac{5}{2}}-5n^{3} by 8m^{\frac{5}{2}}-5n^{3} and combine like terms.

$$-64m^{5}+25n^{6}$$

Differentiate w.r.t. m

$$-320m^{4}$$