Question

Simplify. Final answers should be written in standard form. Number 16

Answer 1

First, we compute the product of the first two binomials:

$\begin{gathered} (a+b)(3a-b)=3a\cdot a-b\cdot a+3a\cdot b-b\cdot b \\ =3a^2+2ab-b^2. \end{gathered}$

Now, we multiply the above result with the last binomial:

$\begin{gathered} (3a^2+2ab-b^2)(2a+7b)=2a\cdot3a^2+2a\cdot2ab-b^2\cdot2a+3a^2\cdot7b+2ab\cdot7b-b^2\cdot7b \\ =6a^3+4a^2b-2b^2a+21a^2b+14ab^2-7b^3\text{.} \end{gathered}$

Finally, we simplify:

$6a^3+4a^2b-2b^2a+21a^2b+14ab^2-7b^3=6a^3+25a^2b+12b^2a-7b^3.$

Answer:

$6a^3+25a^2b+12b^2a-7b^3$