Chapter 8.2, Problem 2BGP

To determine

To simplify: The expression $15t\left(10y^3{t}^5+5y^{2}t\right)-2y\left(y{t}^2+4y^2\right)$

Answer to Problem 2BGP

  $150t^6{y}^3+73y^2{t}^2-8y^3$

Explanation of Solution

Given:

  $15t\left(10y^3{t}^5+5y^{2}t\right)-2y\left(y{t}^2+4y^2\right)$

Calculation:

The given expression is $15t\left(10y^3{t}^5+5y^{2}t\right)-2y\left(y{t}^2+4y^2\right)$

Remove the parenthesis

  $150t^6{y}^3+75y^2{t}^2-2y^2{t}^2-8y^3$

Group the like terms

  $150t^6{y}^3+\left(75y^2{t}^2-2y^2{t}^2\right)-8y^3$

Combine the like terms

  $150t^6{y}^3+73y^2{t}^2-8y^3$