Question

How do you simplify $9k-3k$ ?

Answer 1

Hint: We have been given an expression which consists of two terms of the k-variable which have power 1 that is linear terms. Here, we shall notice that both the terms consist of the k-variable which has the same power. Thus, we can take this k-variable common and perform the mathematical operation on the remaining terms. After subtracting the remaining constant terms, we will obtain the simplest form of the given expression.

Complete step by step solution:
Given that \[9k-3k\].
We know that while simplifying mathematical expressions and equations, only like terms are taken common which consist of the same variables or same constants raised to same powers.
Here in both the terms of the expression \[9k-3k\], $k$ is occurring. Thus, we shall take it common and get
\[\Rightarrow 9k-3k=\left( 9-3 \right)k\]
Now, we will subtract the integers remaining in the bracket. Subtracting 3 from 9, we get
\[\Rightarrow 9k-3k=6k\]

Therefore, the given expression \[9k-3k\] is simplified to \[6k\] by using a simple grouping method of algebraic terms.

Note: Likewise, on any number of like terms with same exponential power, all the mathematical operations like addition, subtraction, multiplication and division can be performed easily. However, grouping and taking common terms can be done for like terms with different exponential powers also. We will take the term common which would be assigned the smaller power of the two powers. Then the term with the larger power out of the two would be modified as the smaller power would have been subtracted from the larger one. This is because taking a term common is similar to multiplying and dividing the entire expression with that term.