Let us multiply the given binomials (2x^2 5y^2) and #160; (x^2+3y^2) #160;as shown below: (2x^ 2 5y^ 2 )(x^ 2 +3y^ 2 ) =2x^ 2 (x^ 2 +3y ...

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Multiplication of Any Polynomial

2x2-5y2×x2+3y...

Question

$(2 x^{2} - 5 y^{2}) \times (x^{2} + 3 y^{2})$ .

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Solution

Let us multiply the given binomials $(2 x^{2} - 5 y^{2})$ and $(x^{2} + 3 y^{2})$ as shown below:

$(2 x^{2} - 5 y^{2}) (x^{2} + 3 y^{2}) = 2 x^{2} (x^{2} + 3 y^{2}) - 5 y^{2} (x^{2} + 3 y^{2}) = (2 x^{2} \times x^{2}) + (2 x^{2} \times 3 y^{2}) - (5 y^{2} \times x^{2}) - (5 y^{2} \times 3 y^{2}) = 2 x^{4} + 6 x^{2} y^{2} - 5 x^{2} y^{2} - 15 y^{4} = 2 x^{4} + (6 x^{2} y^{2} - 5 x^{2} y^{2}) - 15 y^{4} (C o m b i n i n g l i k e t e r m s) = 2 x^{4} + x^{2} y^{2} - 15 y^{4}$

Hence, $(2 x^{2} - 5 y^{2}) \times (x^{2} + 3 y^{2}) = 2 x^{4} + x^{2} y^{2} - 15 y^{4}$ .

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