Question

How do you factor by grouping : ${r^2} - 20tw + 4wr - 5tr$?

Answer 1

Hint: You need to know the definition of factorization by grouping which is nothing but getting the common factors out by grouping the expression. Sticking to the definition try making groups of the given expression and taking the common factor out up to the point where no common factor exists anymore.

Complete step by step answer:
As asked in the question we need to solve the given equation by grouping. For this we need to understand the concept of grouping.
It simply means that we just have to bring together the terms with common factors before factoring.
Let’s start doing the same with the given expression.
So in the expression ${r^2} - 20tw + 4wr - 5tr$ we will group ${r^2}$and $ - 5tr$ together and $ - 20tw$ and $4wr$respectively.
So writing this in the expression form we get
${r^2} - 5tr - 20tw + 4wr$
So from the first group i.e. ${r^2} - 5tr$, factor out r
So we get, $r\left( {r - 5t} \right) - 20tw + 4wr$
Also factor out 4w from the second group, we get
$r\left( {r - 5t} \right) + 4w\left( {r - 5t} \right)$
Again factor out the common terms from the above and we get
$\left( {r - 5t} \right)\left( {r + 4w} \right)$
This will be the final grouping of the given expression.

Note: this could have been the simplest example of factorization by grouping as there can be many complicated situations that sometimes exist in the expression. But the process of solving remains the same even in the complications. Quadratic equations can also be solved by this process of grouping.