Solve -5a^2(-b)+(-3b)(+2a^2)-(+8a)(+5ab)+30a^2b

$$- 5 a ^ { 2 } ( - b ) + ( - 3 b ) ( + 2 a ^ { 2 } ) - ( + 8 a ) ( + 5 a b ) + 30 a ^ { 2 } b$$

Evaluate

$$-11ba^{2}$$

Solution Steps

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

$$-5a^{2}\left(-b\right)-3b\times 2a^{2}-8a^{2}\times 5b+30a^{2}b$$

Multiply -5 and -1 to get 5.

$$5a^{2}b-3b\times 2a^{2}-8a^{2}\times 5b+30a^{2}b$$

Multiply -3 and 2 to get -6.

$$5a^{2}b-6ba^{2}-8a^{2}\times 5b+30a^{2}b$$

Combine 5a^{2}b and -6ba^{2} to get -a^{2}b.

$$-a^{2}b-8a^{2}\times 5b+30a^{2}b$$

Multiply 8 and 5 to get 40.

$$-a^{2}b-40a^{2}b+30a^{2}b$$

Combine -a^{2}b and -40a^{2}b to get -41a^{2}b.

$$-41a^{2}b+30a^{2}b$$

Combine -41a^{2}b and 30a^{2}b to get -11a^{2}b.

$$-11a^{2}b$$

Differentiate w.r.t. a

$$-22ab$$