Chapter 8.3, Problem 11CYU

To determine

To find: The product $\left(2n^2+3n-6\right)\left(5n^2-2n-8\right)$

Answer to Problem 11CYU

  $10n^4+11n^3-52n^2-12n+48$

Explanation of Solution

Given:

  $\left(2n^2+3n-6\right)\left(5n^2-2n-8\right)$

Calculation:

Multiply each term of the first polynomial with the each term of the second polynomial

  $\begin{array}{l}\left(2n^2+3n-6\right)\left(5n^2-2n-8\right)\\ =2n^2\cdot 5n^2+2n^2\cdot \left(-2n\right)+2n^2\cdot \left(-8\right)+3n\cdot 5n^2+3n\cdot \left(-2n\right)+3n\cdot \left(-8\right)-6\cdot 5n^2-6\cdot \left(-2n\right)-6\cdot \left(-8\right)\\ =10n^4-4n^3-16n^2+15n^3-6n^2-24n-30n^2+12n+48\\ =10n^4+11n^3-52n^2-12n+48\end{array}$

So, the product of the polynomial is $10n^4+11n^3-52n^2-12n+48$