Question

How do you factor $x{{y}^{2}}+{{x}^{2}}{{y}^{3}}$ ?

Answer 1

Hint: In this question, we have to find the factors of an algebraic expression. So, we will use the basic mathematical rules to get the required solution. We start solving this problem by taking common xy from the given algebraic expression. Then, we will again take common y from the two terms which lies within the brackets. In the last, we will make the necessary calculation, to get the required solution to the problem.

Complete step by step solution:
According to the question, we have to find the factors of an algebraic expression.
So, we will apply the basic mathematical rules to get the required result.
The expression given to us is $x{{y}^{2}}+{{x}^{2}}{{y}^{3}}$ ---------------- (1)
Now, we start solving our problem by taking the common xy from the equation (1), we get
$\Rightarrow xy\left( y+x{{y}^{2}} \right)$
Now, we see that in the brackets we have y common in both the terms. Therefore, we will take y common from the two terms which lies within the brackets, we get
$\Rightarrow xy\left( y\left( 1+xy \right) \right)$
So, we will solve further the above expression, we get
$\Rightarrow x{{y}^{2}}\left( 1+xy \right)$ which is the required solution.
Therefore, for the algebraic expression $x{{y}^{2}}+{{x}^{2}}{{y}^{3}}$ , its factors are equal to $\left( x{{y}^{2}} \right)\left( 1+xy \right)$ .

Note: While solving this equation, do mention all the steps properly to avoid any confusion and mathematical errors. One of the alternative methods to solve this problem is to take the common $x{{y}^{2}}$ from the given expression to get the required result for the problem. Also, you can check your answer by using the distributive property in the solution, which is equal to the expression given in the problem.