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Identity (x+y)^2

Add the follo...

Question

Add the following expressions:

$(i i)$ $\begin{matrix} - x^{2} - 3 x y + 3 y^{2} + 8, 3 x^{2} - 5 y^{2} - 3 + 4 x y and - 6 x y + 2 x^{2} - 2 + y^{2} \end{matrix}$

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Solution

$Step:$ Find the sum

By grouping the terms having the same literals and adding, we get,

$\begin{matrix} (- x^{2} - 3 x y + 3 y^{2} + 8) + (3 x^{2} - 5 y^{2} - 3 + 4 x y) + (- 6 x y + 2 x^{2} - 2 + y^{2}) \end{matrix}$

$= - x^{2} - 3 x y + 3 y^{2} + 8 + 3 x^{2} - 5 y^{2} - 3 + 4 x y - 6 x y + 2 x^{2} - 2 + y^{2}$

$= (- x^{2} + 3 x^{2} + 2 x^{2}) + (- 3 x y + 4 x y - 6 x y) + (3 y^{2} - 5 y^{2} + y^{2}) + (8 - 3 - 2)$

$= x^{2} (- 1 + 3 + 2) + x y (- 3 + 4 - 6) + y^{2} (3 - 5 + 1) + (8 - 3 - 2)$

$= 4 x^{2} - 5 x y - y^{2} + 3$

Hence, the sum of the given terms is $4 x^{2} - 5 x y - y^{2} + 3$

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Identity (x+y)^2

Standard IX Mathematics

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