Add the following algebraic expressions:
$32 a^{2} + 21 a b + 16 b^{2}$ , $5 a^{2} + 2 a b + 3 b^{2}$ and $4 a b + b^{2}$

37 a^{2} + 27 a b + 20 b^{2}

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37 a^{2} + 23 a b + 20 b^{2}

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35 a^{2} + 27 a b + 20 b^{2}

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37 a^{2} + 27 a b + 19 b^{2}

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Solution

The correct option is A $37 a^{2} + 27 a b + 20 b^{2}$
$Column Method: - ------------------- -$
In column method, we would arrange the like terms parallely and add them.
This can be shown as:

The value of the sum of the given algebraic expressions is $37 a^{2} + 27 a b + 20 b^{2} - ------------------- - .$

$Horizontal Method: - ----------------------- -$
We are having three algebraic expressions as $32 a^{2} + 21 a b + 16 b^{2}$ , $5 a^{2} + 2 a b + 3 b^{2}$ and $4 a b + b^{2}$ .
We need to add them.

This can be done as:
$(32 a^{2} + 21 a b + 16 b^{2})$ $+$ $(5 a^{2} + 2 a b + 3 b^{2})$ $+$ $(4 a b + b^{2})$

Now, combining the like terms together:
$= (32 a^{2} + 5 a^{2}) + (21 a b + 2 a b + 4 a b)$ $+ (16 b^{2} + 3 b^{2} + b^{2})$
Adding the like terms:

$= 37 a^{2} + 27 a b + 20 b^{2}$

The value of the sum of the given algebraic expressions is $37 a^{2} + 27 a b + 20 b^{2} - ------------------- - .$

Therefore, option (a.) is the correct answer.

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