Question

Find the LCM of set of polynomials $x^2-y^2,x^3+x^{2}y$.

Short answer

The LCM of given polynomials is $x^2\left(x-y\right)\left(x+y\right)$.

Step-by-step solution

Step 1. Write down the given polynomials.

The given polynomials are $x^2-y^2,x^3+x^{2}y$.

Step 2. Factorize the polynomials and take common factors of each higher power.

The polynomial $x^2-y^2$ is factorized as: $\left(x-y\right)\left(x+y\right)$

The polynomial $x^3+x^{2}y$ is factorized as: $x^2\left(x+y\right)$

Taking common factors of each higher power, the LCM of given polynomials is written as:

$\begin{array}{l}LCM=\left(x-y\right)\left(x+y\right)\left(x^2\right)\\ =x^2\left(x-y\right)\left(x+y\right)\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $x^2\left(x-y\right)\left(x+y\right)$.