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Chapter 9: Q19. (page 483)

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

Short Answer

Expert verified

The LCM of given polynomials is $x^{2} (x - y) (x + y)$ .

Step by step solution

01

Step 1. Write down the given polynomials.

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

02

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

The polynomial $x^{2} - y^{2}$ is factorized as: $(x - y) (x + y)$

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

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

$\begin{array}{l} L C M = (x 鈭� y) (x + y) (x^{2}) \\ = x^{2} (x 鈭� y) (x + y) \end{array}$

03

Step 3. Conclusion.

The LCM of given polynomials is $x^{2} (x - y) (x + y)$ .

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