Question

Add: $10x+4xy+6x^{2}y+5x{y}^2+12y$ and $4x-3xy+2x^{2}y-4x{y}^2-5y$

• A. $14x+xy+8x{y}^2+x{y}^2+y$
• B. $14x+7xy+x{y}^2+x{y}^2+7y$
• C. $14x+xy+8x{y}^2+x{y}^2+7y$
• D. $14x+7xy+8x{y}^2+x{y}^2+7y$

Answer 1

The correct option is C $14x+xy+8x{y}^2+x{y}^2+7y$

$\underset{–}{\text{Column Method:}}$
Applying the Column Method for addition of these two expressions. In this method, we write like terms parallely and add them.

This can be shown as:


The value of the sum of the algebraic expressions $10x+4xy+6x^{2}y+5x{y}^2+12y$ and $4x-3xy+2x^{2}y-4x{y}^2-5y$ is $\underset{–}{14x+xy+8x{y}^2+x{y}^2+7y}$.


$\underset{–}{\text{Horizontal Method:}}$
Addition of the two given algebraic expressions can be shown as:

$(10x+4xy+6x^{2}y+5x{y}^2+12y)$ $+$ $(4x-3xy+2x^{2}y-4x{y}^2-5y)$

Combining the like terms together:
$=(10x+4x)+(4xy-3xy)+(6x^{2}y+2x^{2}y)$ $+$ $(5x{y}^2-4x{y}^2)+(12y-5y)$

Adding the like terms:
$=\underset{–}{(10x+4x)}+\underset{–}{(4xy-3xy)}+\underset{–}{(6x^{2}y+2x^{2}y)}$ $+$ $\underset{–}{(5x{y}^2-4x{y}^2)}+\underset{–}{(12y-5y)}$
$=14x+xy+8x{y}^2+x{y}^2+7y$

The value of the sum of the algebraic expressions $10x+4xy+6x^{2}y+5x{y}^2+12y$ and $4x-3xy+2x^{2}y-4x{y}^2-5y$ is $\underset{–}{14x+xy+8x{y}^2+x{y}^2+7y}.$

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