Question

How do you simplify the algebraic expression $6{x^3} + 7{x^3}$?

Answer 1

Hint: In this question, we need to simplify the given algebraic expression. Note that here we are given a very simple expression and it is easy to simplify. Note that there are two terms which need to be added. Since the exponential ${x^3}$ is common for both the terms, we factor it out. Then we just need to add the coefficients of ${x^3}$ which are numbers and simplify it. Then we obtain the required simplified form.

Complete step-by-step solution:
Given an expression of the form $6{x^3} + 7{x^3}$
We are asked to simplify the above algebraic expression.
Firstly, let us understand what exactly is an algebraic expression.
An algebraic expression has numbers, symbols and variables. It is built up from integer constants, variables and the mathematical operations such as addition, subtraction, multiplication and division.
For example, $5{x^2} - 25xy$ is an example for an algebraic expression.
Note that these expressions are represented with the help of unknown variables, constants and coefficients. An algebraic expression has no sides or equal to sign.
Consider the given algebraic expression $6{x^3} + 7{x^3}$ …… (1)
Note that here x is a variable, whose value is unknown to us which can take any value.
The numbers 6 and 7 are known as the coefficient of ${x^3}$, as they are constant values used with the variable term.
Note that the variable x is raised to the power 3 and the exponential ${x^3}$ is a common term in the given expression. So this makes the problem very easy to simplify and solve.
Now we factor out the common term ${x^3}$ from the equation (1), we get,
$ \Rightarrow {x^3}(6 + 7)$
Now we have numbers inside the parenthesis. We just simply add the numbers to obtain the solution.
Adding the numbers inside the parenthesis we get,
$ \Rightarrow {x^3}(13)$
This can be written as $13{x^3}$.
Hence the simplified form of the expression $6{x^3} + 7{x^3}$ is $13{x^3}$.

Note: If we have any common term in the given expression, we just factor it out and simplify the expression for the rest terms. Students must be careful while factoring out the term. Since it is very simple to solve, they should not make any mistakes in simplifying. We have to separate variables from the constant terms, to make it easier.
Note that algebraic expressions are represented with the help of unknown variables, constants and coefficients. An algebraic expression has no sides or equal to sign.