State whether statement is true or false
Subtracting the second expression from the first expression,we get
$(5 x^{2} - 3 x y - 7 y^{2}) - (3 x^{2} - x y - 2 y^{2}) = 2 x^{2} - 2 x y - 5 y^{2}$

True

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False

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Solution

The correct option is A True
The given two expressions are $(5 x^{2} - 3 x y - 7 y^{2})$ and $(3 x^{2} - x y - 2 y^{2})$ .

Let us subtract the second expression from the first expression as shown below:

$(5 x^{2} - 3 x y - 7 y^{2}) - (3 x^{2} - x y - 2 y^{2}) = 5 x^{2} - 3 x y - 7 y^{2} - 3 x^{2} + x y + 2 y^{2} = (5 x^{2} - 3 x^{2}) + (- 3 x y + x y) + (- 7 y^{2} + 2 y^{2}) (C o m b i n i n g l i k e t e r m s) = (5 - 3) x^{2} + (- 3 + 1) x y + (- 7 + 2) y^{2} = 2 x^{2} - 2 x y - 5 y^{2}$

Hence, $(5 x^{2} - 3 x y - 7 y^{2}) - (3 x^{2} - x y - 2 y^{2}) = 2 x^{2} - 2 x y - 5 y^{2}$ .

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