Chapter 8.2, Problem 37PPS

To determine

To simplify the given expression.

Answer to Problem 37PPS

  $2\left(10n{p}^4+3n^3{p}^3-4n{p}^2\right)$

Explanation of Solution

Given:

  $\frac{2}{3}n{p}^2\left(30p^2+9n^{2}p-12\right)$

Calculation:

Solving the given expression,

  $\Rightarrow \frac{2}{3}n{p}^2\left(30p^2+9n^{2}p-12\right)$

  $\Rightarrow \frac{2}{3}n{p}^2\cdot 30p^2+\frac{2}{3}n{p}^2\cdot 9n^{2}p+\frac{2}{3}n{p}^2\cdot \left(-12\right)$   [Solving the bracket]

  $\Rightarrow 20n{p}^4+6n^3{p}^3-8n{p}^2$

  $\Rightarrow 2\left(10n{p}^4+3n^3{p}^3-4n{p}^2\right)$

Conclusion:

Therefore, after simplification, the answer is $2\left(10n{p}^4+3n^3{p}^3-4n{p}^2\right)$ .