Chapter R3, Problem 1E

To determine

Combine the like terms in the given expression.

Answer to Problem 1E

Solution: We get the final answer as $8x^3$ .

Explanation of Solution

Explanation:Given: The expression: $3x^3+5x^3$

Concept used: Like terms are the terms which have same variable portions. Only the coefficients can be different. For example:

$2x$ and $5x$ are like terms because the variable $x$ in both the terms has exponent 1.

  $x^2$ and $3x^2$ are like terms because the variable $x$ in both the terms has exponent 2.

  $3x{y}^2$ and $7x{y}^2$ are like terms because the variables $x$ and $y$ have same exponent in both the terms.

While adding/subtracting like terms, we keep the variable portion as it is and add/subtract the corresponding coefficients.

Calculation: We have been given the expression $3x^3+5x^3$ .

We can see that the variable $x$ in both the terms have same exponent. Therefore, we can combine the coefficients.

  $\begin{array}{l}3x^3+5x^3=(3+5)x^3\\ 3x^3+5x^3=(8)x^3\\ 3x^3+5x^3=8x^3\end{array}$

Conclusion: On combining the like terms, we get the final expression as $8x^3$ .