Chapter 8.2, Problem 25PPS

To determine

To simplify the given expression.

Answer to Problem 25PPS

  $-4\left(2a^3-5a^2-a+3\right)$

Explanation of Solution

Given:

  $a\left(-8a^2+2a+4\right)+3\left(6a^2-4\right)$

Calculation:

Solving the given expression,

  $\Rightarrow a\left(-8a^2+2a+4\right)+3\left(6a^2-4\right)$

  $\Rightarrow a\cdot \left(-8a^2\right)+a\cdot 2a+a\cdot 4+3\cdot 6a^2+3\cdot \left(-4\right)$

  $\Rightarrow -8a^3+2a^2+4a+18a^2-12$

  $\Rightarrow -8a^3+2a^2+18a^2+4a-12$

  $\begin{array}{l}\Rightarrow -8a^3+20a^2+4a-12\\ \Rightarrow -4\left(2a^3-5a^2-a+3\right)\end{array}$

Conclusion:

Therefore, after simplification, the answer is $-4\left(2a^3-5a^2-a+3\right)$ .