Question #19780

2 Answers
Feb 13, 2018

The answer is A

Explanation:

A because ;

Step 1
You open the brackets or parentheses so that the equation becomes

6x^3y^3+5x^2y^2-x^2y+xy^2+3x+2+x^3y^3 x^2y^2+x^2y+3x+4

While open the brackets , take care of the signs

Step 2

Add or subtract the like terms

And , you get A as the answer

Feb 13, 2018

7x^3y^3+4x^2y^2+xy^2+6x-2

Option \ \ \ A \ \ \ is the right choice.

Explanation:

The terms of an expression are the parts of a mathematical expression that are separated by a plus (+) or minus (–) sign. Each term is either a number or the product of a number (sometimes an understood 1\ ) and one or more variables.

For example: \ \ \ 7x^3-14x^2-8x-3x^3+9

The above mentioned experssion have five terms.

Terms are like terms if their variable parts are the same. In the above expression, 7x^3 \ \ \ and\ \ \ -3x^3 are like terms. -14x^2\ \ \ ,\ \ 18x\ \ \ and \ 9\ are unlike terms.

So, let's start our problem!

(6x^3y^3+5x^2y^2-x^2y+xy^2+3x+2)-(-x^3y^3+x^2y^2-x^2y-3x+4)

Remove parantheses \ \ \ (a)=a:

=6x^3y^3+5x^2y^2-x^2y+xy^2+3x+2-(-x^3y^3+x^2y^2-x^2y-3x+4)

Distribute the parantheses on the right as:

=6x^3y^3+5x^2y^2-x^2y+xy^2+3x+2-(-x^3y^3)-(x^2y^2)-(-x^2y)-(-3x)-(4)

Remember the important parantheses rule in algebra stated as:

-(-a)=a\ \ \ \ \ \ and \ \ \ \ \ \ -(a)=-a

By applying here, we get:

=6x^3y^3+5x^2y^2-x^2y+xy^2+3x+2+x^3y^3-x^2y^2+x^2y+3x-4

Next step is to group the like terms:

=6x^3y^3+x^3y^3+5x^2y^2-x^2y-x^2y^2+x^2y+xy^2+3x+3x+2-4


Add the similar terms \ \ \ 3x+3x=6x , so as to get:

=6x^3y^3+x^3y^3+5x^2y^2-x^2y-x^2y^2+x^2y+xy^2+6x+2-4


Add the similar terms \ \ \ -x^2y+x^2y=0 , so as to get:

=6x^3y^3+x^3y^3+5x^2y^2-x^2y^2+xy^2+6x+2-4


Add the similar terms\ \ \ 5x^2y^2-x^2y^2=4x^2y^2 , so as to get:

=6x^3y^3+x^3y^3+4x^2y^2+xy^2+6x+2-4


Add the similar terms\ \ \ \:6x^3y^3+x^3y^3=7x^3y^3 , so as to get:

=7x^3y^3+4x^2y^2+xy^2+6x+2-4


Add/Subtract the numbers \ \ \ 2-4=-2, so as to get:

=7x^3y^3+4x^2y^2+xy^2+6x-2