Question

How do you factor \[3.375{{v}^{3}}+15.625{{r}^{6}}\] ?

Answer 1

Hint: We have an expression with two terms. To factor it, we have to take out common terms. There are 2 variables v and r in two terms and we cannot take common variables. So, we look for common constants and then take them out. Once we have taken the common constants out we will have our factored form of the expression and the final answer.

Complete step by step solution:
Before solving, let us understand concepts. Solving such problems requires some basic understanding of the various sub-topics of factorisation like, factor theorem, vanishing factors and hit and trial method. These methods come very handy when we are given any complex problems or we are in some circumstances where we cannot proceed further.
We should keep one very important thing in mind, that is, only the like terms of an equation can be taken together and the basic math operations can only be applied on the like terms. We cannot add or subtract two unlike terms, however we can multiply or divide two unlike terms. In this given problem we can very clearly see that there are only two terms in this equation and both the terms are unlike.
Now we start off with the solution to the problem by writing that we take 3.375 common from the equation, as there are two different types of parameters present in this equation, we cannot take anything common further. Thus we can evaluate this and write,
\[\Rightarrow 3.375\left( {{v}^{3}}+4.63{{r}^{6}} \right)\]
Thus this will be our answer to the problem. \[3.375\left( {{v}^{3}}+4.63{{r}^{6}} \right)\] .

Note: This problem consists of some basic as well as to some extent advanced concepts of factorisation like factor theorem, remainder theorem and a lot other. A given equation may be homogeneous or heterogeneous, which means, there may be only one unknown parameter or may be many unknown parameters respectively. However we must keep one very important thing in mind, that is, only one type of parameters can be grouped together to perform various mathematical operations.