Question

Question #19780

Answer 1

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

Answer 2

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

Option `\ \ \`A `\ \ \` is the right choice.
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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!
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`(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`

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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`

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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`

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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`

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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`

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

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