Solve 2ab*(-a^{3}b)+[ab^{2}*(-3a^2b)]-5a^3b*ab+ab*a^2b^2=

$$2 a b \cdot ( - a ^ { 3 } b ) + [ a b ^ { 2 } \cdot ( - 3 a ^ { 2 } b ) ] - 5 a ^ { 3 } b \cdot a b + a b \cdot a ^ { 2 } b ^ { 2 } =$$

Factor

$$-\left(7a+2b\right)b^{2}a^{3}$$

Solution Steps

Factor out ab.

$$ab\left(-2a^{3}b-3ba^{2}b-5a^{2}ab+a^{2}b^{2}\right)$$

Consider -2a^{3}b-3a^{2}b^{2}-5ba^{3}+a^{2}b^{2}. Factor out a^{2}b.

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

Consider -2a-3b-5a+b. Multiply and combine like terms.

$$-7a-2b$$

Rewrite the complete factored expression.

$$aba^{2}b\left(-7a-2b\right)$$

Evaluate

$$-\left(7a+2b\right)b^{2}a^{3}$$