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(x+y)^2 + (x-y)^2 and (x+y)^2 - (x-y)^2

Question 39In...

Question

Question 39

In the question given below, fill in the blank to make the statement true:

$(a - b)^{2} +$ ___ $= a^{2} - b^{2}$

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Solution

$2 a b - 2 b^{2}$
Let $(a - b)^{2} + x = a^{2} - b^{2}$
$\Rightarrow a^{2} + b^{2} - 2 a b + x = a^{2} - b^{2} [∵ (a - b)^{2} = a^{2} + b^{2} - 2 a b] \Rightarrow x = a^{2} - b^{2} - (a^{2} + b^{2} - 2 a b) = a^{2} - b^{2} - a^{2} - b^{2} + 2 a b = 2 a b - 2 b^{2}$

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(x+y)^2 + (x-y)^2 and (x+y)^2 - (x-y)^2

Standard VIII Mathematics

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