Multiply: $(2 x^{2} - 3 x y + y^{2})$ by $(2 y^{2} - x y - x^{2})$
Answer: $6 x^{2} y^{2} + x^{3} y - 7 x y^{3} + 2 y^{4} - 2 x^{4}$

True

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False

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Solution

The correct option is A True

Given:
$\Rightarrow (2 x^{2} - 3 x y + y^{2}) \times (2 y^{2} - x y - x^{2})$

multply term by term and add:

$= 2 x^{2} (2 y^{2} - x y - x^{2}) - 3 x y (2 y^{2} - x y - x^{2}) + y^{2} (2 y^{2} - x y - x^{2})$

$= 4 x^{2} y^{2} - 2 x^{3} y - 2 x^{4} - 6 x y^{3} + 3 x^{2} y^{2} + 3 x^{3} y + 2 y^{4} - x y^{3} - x^{2} y^{2}$

$= 6 x^{2} y^{2} - x^{3} y - 7 x y^{3} + 2 y^{4} - 2 x^{4}$

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