Question

How do you factor completely $ xy + 2x + 4y + 8 $ ? $ xy + 2x + 4y + 8 $

Answer 1

Hint: Even though there can be different ways of finding the solution, we will stick to the method of factorization by grouping. All you have to do is make a group of terms containing common factors and keep continuing this process until it is impossible to further find common factors from the obtained result.

Complete step-by-step answer:
We will choose the easier method to solve this question.
i.e. factorization by grouping.
All we have to do in this method is make groups of two of the terms which have a common factor in them and take out common factors up to the part where nothing more common can be taken out.
We will start as follows:
The expression given to us is $ xy + 2x + 4y + 8 $
Therefore $ xy + 2x + 4y + 8 $ = $ \left( {xy + 2x} \right) + \left( {4y + 8} \right) $
 $ = x\left( {y + 2} \right) + 4\left( {y + 2} \right) $
Now again taking common factors out we get
 $ xy + 2x + 4y + 8 $ $ = \left( {y + 2} \right)\left( {x + 4} \right) $
after this step you cannot further factorize the expression and hence this will be the final factorization.
Hence we have succeeded in factoring the given expression to us completely.
So, the correct answer is “ $ \left( {y + 2} \right)\left( {x + 4} \right) $ ”.

Note: This process of factorization by grouping is often and commonly used while solving quadratic equations. It is one of the basic methods but has it’s own set of limitations. This method is widely used in different parts of algebra in mathematics to solve the problems as done in above sum.