As the number of items you provided for the said task exceeded three, I'll just provide you the answers and solutions to the even-numbered items. These will help you to visualize what you need to do to answer the rest of the equations.
Note: In Mathematics, you learn when you practice solving.
2. [tex]\bold{(8x+3y)+(x-y)+(6x+1)}[/tex]
[Sol]
Distribute the signs for each grouped term. Rewriting,
[tex]= 8x+3y+x-y+6x+1[/tex]
Notice that some terms have the same variables (these stand for the letters with no given value yet such as the [tex]x[/tex] and [tex]y[/tex]). Remember, you can add and subtract those having the same variables. Thus,
[tex]\text{Add the bolded terms.}\\= \bold{8x}+3y+\bold{x}-y+\bold{6x}+1\\=15x+\bold{3y}-\bold{y}+1[/tex]
Distribute the signs for each grouped term. Since we have a negative sign before the second group of terms, take note that a (-) integer times a (+) integer results in a (-) integer while a (-) integer times another (-) integer equals a (+) integer. It follows the rule of like signs are positive and unlike signs are negative. Rewriting,
[tex]=5m^2+2m-3-6m^2-3x+7\\\text{Proceed to addition or subtraction,}\\\therefore,\ =\boxed{\bold{-m^2+2m-3x+4}}[/tex]
Answers & Comments
Adding, Subtracting, and Dividing Polynomials
As the number of items you provided for the said task exceeded three, I'll just provide you the answers and solutions to the even-numbered items. These will help you to visualize what you need to do to answer the rest of the equations.
Note: In Mathematics, you learn when you practice solving.
2. [tex]\bold{(8x+3y)+(x-y)+(6x+1)}[/tex]
[Sol]
Distribute the signs for each grouped term. Rewriting,
[tex]= 8x+3y+x-y+6x+1[/tex]
Notice that some terms have the same variables (these stand for the letters with no given value yet such as the [tex]x[/tex] and [tex]y[/tex]). Remember, you can add and subtract those having the same variables. Thus,
[tex]\text{Add the bolded terms.}\\= \bold{8x}+3y+\bold{x}-y+\bold{6x}+1\\=15x+\bold{3y}-\bold{y}+1[/tex]
[tex]\therefore\ =\boxed{\bold{15x+2y+1}}[/tex]
4. [tex]\bold{(-mn^2+10mn+m^2n)+(mn^2+3mn-m^2n)}[/tex]
[Sol]
Distribute the signs for each grouped term. Rewriting,
[tex]=-mn^2+10mn+m^2n+mn^2+3mn-m^2n[/tex]
Follow the steps in item #2.
[tex]=\bold{-mn^2}+10mn\bold{+m^2n}+mn^2+3mn-m^2n\\=10mn+\bold{mn^2}+3mn-\bold{m^2n}\\=10mn+3mn[/tex]
[tex]\therefore\ = \boxed{\bold{13mn}}[/tex]
6. [tex]\bold{(5m^2+2m-3)-(6m^2+3x-7)}[/tex]
[Sol]
Distribute the signs for each grouped term. Since we have a negative sign before the second group of terms, take note that a (-) integer times a (+) integer results in a (-) integer while a (-) integer times another (-) integer equals a (+) integer. It follows the rule of like signs are positive and unlike signs are negative. Rewriting,
[tex]=5m^2+2m-3-6m^2-3x+7\\\text{Proceed to addition or subtraction,}\\\therefore,\ =\boxed{\bold{-m^2+2m-3x+4}}[/tex]
8. [tex]\bold{(4y^2-7y)-(-6y^2+5y-7)}[/tex]
[Sol]
Same steps as previous items.
[tex]=4y^2-7y+6y^2-5y+7\\\therefore\ =\boxed{\bold{10y^2-12y+7}}[/tex]
10. [tex]\bold{(4p+9)(4p+9)}[/tex]
[Sol]
Use the FOIL method.
[tex]=4p^2+36p+36p+81\\\therefore\ =\boxed{\bold{16p^2+72p+81}}[/tex]
12. [tex]\bold{(-5ab)(2ab^2+4)}[/tex]
[Sol]
Distribute the terms and multiply.
[tex]=(-5ab)(2ab^2)+(-5ab)(4)\\\therefore\ =\boxed{\bold{-10ab^3-20ab}}[/tex]
14. [tex]\bold{\dfrac{6x^4y^2+3x^2y^2-9x^2y}{3x^2y^2}}[/tex]
[Sol]
Rewriting,
[tex]=\dfrac{6x^4y^2}{3x^2y^2}+\dfrac{3x^2y^2}{3x^2y^2}-\dfrac{9x^2y}{3x^2y^2}[/tex]
[tex]\therefore\ =\boxed{\bold{2x^2+1-\dfrac{3}{y}}}\ or\ \boxed{\bold{\dfrac{2x^2y+y-3}{y}}}[/tex]
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To aid you in adding, subtracting, multiplying, and dividing polynomials, you can read the answers to these questions.