State true or false: $2 x y + 4 x^{2} + 5 x y + 5 y^{2} + 16 x^{2}$ is equal to $4 x y + 9 x^{2} + 16 y^{2} .$

4xy + 9x² +16y²

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3xy + 10x² + 5y²

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Solution

The correct answer is F
Like terms contain the same variables raised to the same power.
To check the whether the given expressions are same, we can simplify the two given expressions.
$2 x y + 4 x^{2} + 5 x y + 5 y^{2} + 16 x^{2}$
Add the like terms,
$2 x y, 5 x y$ are like terms. Similarly, $4 x^{2} a n d 16 x^{2}$ are like terms.
$2 x y + 5 x y = 7 x y$ and $4 x^{2} + 16 x^{2} = 20 x^{2}$

$2 x y + 4 x^{2} + 5 x y + 5 y^{2} + 16 x^{2}$
= $20 x^{2} + 5 y^{2} + 7 x y$
It is very clear that $20 x^{2} + 5 y^{2} + 7 x y$ is not equal to $4 x y + 9 x^{2} + 16 y^{2}$

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