Question 4 a What should be added to x2-x y-y2 to obtain 2 x2-3 x y -

Let p should be added. Then according to question, x^2 + xy + y^2 + p = 2x^2 + 3xy ⇒ p = 2x^2 + 3xy (x^2 + xy + y^2) ⇒ p = 2x^2 + 3xy x^2 xy y^2 ⇒ p = 2 ...

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Standard VII

Mathematics

(a-b)^2 Expansion and Visualisation

Question 4 a ...

Question

What should be added to $x^{2} + x y + y^{2}$ to obtain $2 x^{2} + 3 x y$ ?

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Solution

Let $p$ should be added.
Then according to question,
$x^{2} + x y + y^{2} + p = 2 x^{2} + 3 x y$
$\Rightarrow p = 2 x^{2} + 3 x y - (x^{2} + x y + y^{2})$
$\Rightarrow p = 2 x^{2} + 3 x y - x^{2} - x y - y^{2}$
$\Rightarrow p = 2 x^{2} - x^{2} - y^{2} + 3 x y - x y$
$\Rightarrow p = x^{2} - y^{2} + 2 x y$
Hence, $x^{2} - y^{2} + 2 x y$ should be added.

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(a-b)^2 Expansion and Visualisation

Standard VII Mathematics

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What should be added to x2+xy+y2 to obtain 2x2+3xy?

Let p should be added. Then according to question, x2+xy+y2+p=2x2+3xy⇒p=2x2+3xy−(x2+xy+y2)⇒p=2x2+3xy−x2−xy−y2⇒p=2x2−x2−y2+3xy−xy ⇒p=x2−y2+2xy Hence, x2−y2+2xy should be added.

What should be added to $x^{2} + x y + y^{2}$ to obtain $2 x^{2} + 3 x y$ ?