Chapter 8.2, Problem 33PPE

To determine

Towrite:The given expression in standard form.

Answer to Problem 33PPE

The standard form of given expression is $-t^3+t^2+t$ .

Explanation of Solution

Given information:

The given expression is $t^2\left(t+1\right)-t\left(2t^2-1\right)$ .

Methodused:

The standard form of algebraic equation is the expression in decreasing or increasing powers of the variable. Standard form means that the terms are ordered from biggest exponent to lowest exponent.

Calculations:

The given expression is $t^2\left(t+1\right)-t\left(2t^2-1\right)$ .

Simplified form of the expression is

  $t^2\left(t+1\right)-t\left(2t^2-1\right)=t^2\times t+t^2\times 1-t\times 2t^2-t(-1)$  (Product of factors)

  $\Rightarrow t^2\left(t+1\right)-t\left(2t^2-1\right)=t^{2+1}+t^2-2t^{1+2}+t$

  $\Rightarrow t^2\left(t+1\right)-t\left(2t^2-1\right)=t^3+t^2-2t^3+t$

  $\Rightarrow t^2\left(t+1\right)-t\left(2t^2-1\right)=-t^3+t^2+t$   (Re-arranging the terms in decreasing power of t )

Thus, the standard form of given expression is $-t^3+t^2+t$ .

Conclusion:

The standard form of given expression is $-t^3+t^2+t$ .