To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

$\displaystyle 4x^2 + 4x$

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

$\displaystyle 2x + 4y + x^2 + xy$

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

$\displaystyle 2zx$

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

$\displaystyle 2x^3 + x + 1$

To solve, simply combine like terms by adding their coefficients. Thus,

$\displaystyle (2x-8)+(7x-9)=(2+7)x-(8+9)=9x-17$

Adding polynomials is very simple. It's just a matter of collecting like terms. This means that we look to see if there are similar terms that can have their coefficients added. When we can no longer do this, we have reached our final answer.

$\displaystyle (6x^2+x+2)+(x^4+x^2+7)$

$\displaystyle 6x^2+x+2+x^4+x^2+7$

Distributing the plus sign to every term in the polynomial right of the sign, we can omit the parentheses. 

Now we are left to collect like terms until we've reached our final answer.

$\displaystyle {\color{Blue} 6x^2}+{\color{Purple} x}+{\color{Magenta} 2}+x^4{\color{Blue} +x^2}+{\color{Magenta} 7}$

$\displaystyle x^4+{\color{Blue} 7x^2}+{\color{Purple} x}+{\color{Magenta} 9}$ 

Adding polynomials is very simple. It's just a matter of collecting like terms. This means that we look to see if there are similar terms that can have their coefficients added. When we can no longer do this, we have reached our final answer.

$\displaystyle (x^3+4x+2)+(x^2+x+10)$

$\displaystyle x^3+4x+2+x^2+x+10$

Distributing the plus sign to every term in the polynomial right of the sign, we can omit the parentheses. 

Now we are left to collect like terms until we've reached our final answer.

$\displaystyle x^3+{\color{Cyan} 4x}+{\color{Magenta} 2}+{\color{Blue} x^2}+{\color{Cyan} x}+{\color{Magenta} 10}$

$\displaystyle x^3+{\color{Blue} x^2}+{\color{Cyan} 5x}+{\color{Magenta} 12}$ 

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

$\displaystyle 4x^2 + 3x + 8$

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

$\displaystyle 2xy$

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

$\displaystyle 2xz + x - z$