Step 1

The given expression is \(\displaystyle{4}{x}+{6}{x}\)

Since both terms have same variables have equal power (exponent), they are the like terms. To add the terms simply, add the numbers before the variable.

Since, \(\displaystyle{4}+{6}={10}\),

The given expression can be simplified to

\(\displaystyle{4}{x}+{6}{x}={10}{x}\)

The simplified form of the given expression is 10x

Step 2

The given expression is \(\displaystyle{y}-{5}{y}\)

Since both terms have same variables and the variables have equal power (exponent), they are the like terms. To add the terms simply, add the numbers before the variable.

Since, \(\displaystyle{1}-{5}=-{4}\),

the given expression can be simplified to

\(\displaystyle{y}-{5}{y}=-{4}{y}\)

The simplified form of the given expression is -4y.

Step 3

The given expression is \(\displaystyle{3}{x}^{{{2}}}+{5}{x}^{{{2}}}-{2}\)

Here, the like terms are \(\displaystyle{3}{x}^{{{2}}}\) and \(\displaystyle{5}{x}^{{{2}}}\). Combine these two terms by adding the numbers before the variables as follows:

\(\displaystyle{8}{x}^{{{2}}}-{2}\),

The simplified form of the given expression is \(\displaystyle{8}{x}^{{{2}}}-{2}\)

The given expression is \(\displaystyle{4}{x}+{6}{x}\)

Since both terms have same variables have equal power (exponent), they are the like terms. To add the terms simply, add the numbers before the variable.

Since, \(\displaystyle{4}+{6}={10}\),

The given expression can be simplified to

\(\displaystyle{4}{x}+{6}{x}={10}{x}\)

The simplified form of the given expression is 10x

Step 2

The given expression is \(\displaystyle{y}-{5}{y}\)

Since both terms have same variables and the variables have equal power (exponent), they are the like terms. To add the terms simply, add the numbers before the variable.

Since, \(\displaystyle{1}-{5}=-{4}\),

the given expression can be simplified to

\(\displaystyle{y}-{5}{y}=-{4}{y}\)

The simplified form of the given expression is -4y.

Step 3

The given expression is \(\displaystyle{3}{x}^{{{2}}}+{5}{x}^{{{2}}}-{2}\)

Here, the like terms are \(\displaystyle{3}{x}^{{{2}}}\) and \(\displaystyle{5}{x}^{{{2}}}\). Combine these two terms by adding the numbers before the variables as follows:

\(\displaystyle{8}{x}^{{{2}}}-{2}\),

The simplified form of the given expression is \(\displaystyle{8}{x}^{{{2}}}-{2}\)