### Theory:

When multiplying or dividing a monomial by a number, we multiply or divide only its coefficient.
Example:
$\begin{array}{l}6x\cdot 5=30x\phantom{\rule{0.147em}{0ex}};\\ -0,5\mathit{zy}\cdot 2=-\mathit{zy}\phantom{\rule{0.147em}{0ex}};\\ 4{x}^{2}:2=2{x}^{2}\end{array}$
A binomial is an algebraic sum of monomials.
Example:
$\begin{array}{l}3x+2y\phantom{\rule{0.147em}{0ex}};\\ 4\mathit{xy}-6{y}^{2}\end{array}$
When multiplying or dividing a binomial by a number, each term is multiplied or divided.
Example:
$\begin{array}{l}2\cdot \left(2x+4y\right)=4x+8y;\\ \\ \left(-x+{y}^{2}\right)\cdot \left(-3\right)=3x-3{y}^{2};\\ \phantom{\rule{0.147em}{0ex}}\\ \left(6x-4y+c\right):2=\phantom{\rule{0.147em}{0ex}}\\ =3x-2y+\frac{c}{2}=\\ =3x-2y+0,5c.\end{array}$
Actions with the like terms:

$\begin{array}{l}2x+5-x+8y-3y=\\ =\underset{¯}{2x}+5-\underset{¯}{x}+\underset{¯}{\underset{¯}{8y}}-\underset{¯}{\underset{¯}{3y}}=\\ =x+5y+5\end{array}$
Important!
Terms of binomials are often written in brackets. In this case, attention should be paid to the sign in front of the brackets:

$\begin{array}{l}+\left(a+b\right)=a+b\\ -\left(a+b\right)=-a-b\end{array}$

$\begin{array}{l}c-\left(2a-b\right)+2\left(x-y\right)=\\ =c-2a+b+2x-2y\end{array}$