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#