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Addition and Subtraction of Algebraic Expressions

What should b...

Question

Question 5

What should be subtracted from $3 x^{2} - 4 y^{2} + 5 x y + 20$ to obtain $- x^{2} - y^{2} + 6 x y + 20$ ?

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Solution

Let q be the expression to be subtracted.

Then according to the question,

$3 x^{2} - 4 y^{2} + 5 x y + 20 - q = - x^{2} - y^{2} + 6 x y + 20$

$\Rightarrow q = 3 x^{2} - 4 y^{2} + 5 x y + 20 - (- x^{2} - y^{2} + 6 x y + 20)$

$\Rightarrow q = 3 x^{2} - 4 y^{2} + 5 x y + 20 + x^{2} + y^{2} - 6 x y - 20$

$\Rightarrow q = 3 x^{2} + x^{2} - 4 y^{2} + y^{2} + 5 x y - 6 x y + 20 - 20$

$\Rightarrow q = 4 x^{2} - 3 y^{2} - x y + 0$

Hence, $4 x^{2} - 3 y^{2} - x y$ should be subtracted from $3 x^{2} - 4 y^{2} + 5 x y + 20$ to obtain $- x^{2} - y^{2} + 6 x y + 20$ .

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