what is the product?\n$(-6a^{3}b + 2ab^{2})(5a^{2}-2ab^{2}-b)$\n- $-30a^{6}b + 12a^{3}b^{2}+6a^{3}b +…

what is the product?\n$(-6a^{3}b + 2ab^{2})(5a^{2}-2ab^{2}-b)$\n- $-30a^{6}b + 12a^{3}b^{2}+6a^{3}b + 10a^{2}b^{2}-4ab^{4}-2ab^{2}$\n- $-30a^{5}b + 12a^{4}b^{3}+16a^{3}b^{2}-4a^{2}b^{4}-2ab^{3}$\n- $30a^{5}b-12a^{4}b^{3}+4a^{3}b^{2}-4a^{2}b^{4}-2ab^{3}$\n- $30a^{6}b-12a^{3}b^{2}-6a^{3}b + 10a^{2}b^{2}-4ab^{4}-2ab^{2}$

what is the product?\n$(-6a^{3}b + 2ab^{2})(5a^{2}-2ab^{2}-b)$\n- $-30a^{6}b + 12a^{3}b^{2}+6a^{3}b + 10a^{2}b^{2}-4ab^{4}-2ab^{2}$\n- $-30a^{5}b + 12a^{4}b^{3}+16a^{3}b^{2}-4a^{2}b^{4}-2ab^{3}$\n- $30a^{5}b-12a^{4}b^{3}+4a^{3}b^{2}-4a^{2}b^{4}-2ab^{3}$\n- $30a^{6}b-12a^{3}b^{2}-6a^{3}b + 10a^{2}b^{2}-4ab^{4}-2ab^{2}$

Answer

Explanation:

Step1: Use distributive property

[ \begin{align*} &(- 6a^{3}b + 2ab^{2})(5a^{2}-2ab^{2}-b)\ =&-6a^{3}b\times(5a^{2}-2ab^{2}-b)+2ab^{2}\times(5a^{2}-2ab^{2}-b) \end{align*} ]

Step2: Multiply each term

For (-6a^{3}b\times(5a^{2}-2ab^{2}-b)):

[ \begin{align*} -6a^{3}b\times5a^{2}&=-30a^{3 + 2}b=-30a^{5}b\ -6a^{3}b\times(-2ab^{2})&=12a^{3+1}b^{1 + 2}=12a^{4}b^{3}\ -6a^{3}b\times(-b)&=6a^{3}b^{2} \end{align*} ]

For (2ab^{2}\times(5a^{2}-2ab^{2}-b)):

[ \begin{align*} 2ab^{2}\times5a^{2}&=10a^{1+2}b^{2}=10a^{3}b^{2}\ 2ab^{2}\times(-2ab^{2})&=-4a^{1 + 1}b^{2+2}=-4a^{2}b^{4}\ 2ab^{2}\times(-b)&=-2ab^{3} \end{align*} ]

Step3: Combine like - terms

[ \begin{align*} &(-30a^{5}b)+(12a^{4}b^{3})+(6a^{3}b^{2})+(10a^{3}b^{2})+(-4a^{2}b^{4})+(-2ab^{3})\ =&-30a^{5}b + 12a^{4}b^{3}+(6a^{3}b^{2}+10a^{3}b^{2})-4a^{2}b^{4}-2ab^{3}\ =&-30a^{5}b + 12a^{4}b^{3}+16a^{3}b^{2}-4a^{2}b^{4}-2ab^{3} \end{align*} ]

Answer:

(-30a^{5}b + 12a^{4}b^{3}+16a^{3}b^{2}-4a^{2}b^{4}-2ab^{3})