Chapter 8.1, Problem 67PFA

To determine

To find an equivalent expression to the given expression.

Answer to Problem 67PFA

  $6x^2+7x+13$

Explanation of Solution

Given:

Expression: $3x^2+14-(7x-6)+29+(3x^2+5x)+9x$

Concept used:

To find an equivalent expression to the given expression,

1. Combine the terms with like terms.
2. Simplify them using basic arithmetic operations.

Calculation:

Combining the like term in the given expression,

  $\begin{array}{l}\Rightarrow 3x^2+14-(7x-6)+29+(3x^2+5x)+9x\\ \Rightarrow 3x^2+14-7x+6+29+3x^2+5x+9x\\ \Rightarrow (3x^2+3x^2)+(5x+9x-7x)+(29+14)\end{array}$

Simplifying the expression with basic arithmetic operations,

  $\begin{array}{l}\Rightarrow (3x^2+3x^2)+(5x+9x-7x)+(29+14)\\ \Rightarrow 6x^2+7x+13\end{array}$

Conclusion:

The equivalent expression is $6x^2+7x+13.$