Find the value of :
$36 x^{2} + 49 y^{2} + 84 x y$ , when $x = 3, y = 6$

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Solution

$36 x^{2} + 49 y^{2} + 84 x y$
$= {(6 x)}^{2} + {(7 y)}^{2} + 2 \times 6 x \times 7 y$ is of the form $a^{2} + b^{2} + 2 a b$
We have $a^{2} + b^{2} + 2 a b = {(a + b)}^{2}$
From above $a = 6 x$ and $b = 7 y$
$∴ 36 x^{2} + 49 y^{2} + 84 x y = {(6 x + 7 y)}^{2}$
For $x = 3$ and $y = 6$ we have
${(6 \times 3 + 7 \times 6)}^{2} = {(18 + 42)}^{2} = 60^{2} = 3600$

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36 x^{2} + 49 y^{2} + 84 x y

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