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Multiplication of Any Polynomial

Find each of ...

Question

Find each of the following products:

$(3 p^{2} + q^{2}) \times (2 p^{2} - 3 q^{2})$

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Solution

$(3 p^{2} + q^{2}) \times (2 p^{2} - 3 q^{2}) = 3 p^{2} (2 p^{2} - 3 q^{2}) + q^{2} (2 p^{2} - 3 q^{2}) = 6 p^{4} - 9 p^{2} q^{2} + 2 p^{2} q^{2} - 3 q^{4} = 6 p^{4} - 7 p^{2} q^{2} - 3 q^{4}$

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