Chapter 8.2, Problem 28PPS

To determine

To simplify the given expression.

Answer to Problem 28PPS

  $14j^3{k}^2+20j^2{k}^2+10jk-18k^2-27j$

Explanation of Solution

Given:

  $2j\left(7j^2{k}^2+j{k}^2+5k\right)-9\left(-2j^2{k}^2+2k^2+3j\right)$

Calculation:

Solving the given expression,

  $\Rightarrow 2j\left(7j^2{k}^2+j{k}^2+5k\right)-9\left(-2j^2{k}^2+2k^2+3j\right)$

  $\Rightarrow 2j\cdot 7j^2{k}^2+2j\cdot j{k}^2+2j\cdot 5k-9\cdot \left(-2j^2{k}^2\right)-9\cdot 2k^2-9\cdot 3j$

  $\Rightarrow 14j^3{k}^2+2j^2{k}^2+10jk+18j^2{k}^2-18k^2-27j$

  $\Rightarrow 14j^3{k}^2+2j^2{k}^2+18j^2{k}^2+10jk-18k^2-27j$  [Rearranging the terms]

  $\Rightarrow 14j^3{k}^2+20j^2{k}^2+10jk-18k^2-27j$

Conclusion:

Therefore, after simplification, the answer is $14j^3{k}^2+20j^2{k}^2+10jk-18k^2-27j$ .