Find the numerical value of the following expression:
$4 x y - 5 x^{2} y^{2} + 4 x^{3} y^{3}$ if $x = 3$ and $y = 4$

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Solution

Given expression $4 x y - 5 x^{2} y^{2} + 4 x^{3} y^{3}$
Put $x = 3$ and $y = 4$ in the given expression:
$4 x y - 5 x^{2} y^{2} + 4 x^{3} y^{3} = 4 (3) (4) - 5 {(3)}^{2} {(4)}^{2} + 4 {(3)}^{3} {(4)}^{3}$
$= 4 (3) (4) - 5 {(3)}^{2} {(4)}^{2} + 4 {(3)}^{3} {(4)}^{3}$
$= 48 - 5 (9) (16) + 4 (27) (64)$
$= 48 - 720 + 6912$
$= 5520$
Hence the numerical value of expression is $5520 .$

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