# a) Simplify the expression 4x+6x by combining the like terms. NS

a) Simplify the expression $$\displaystyle{4}{x}+{6}{x}$$ by combining the like terms.
b) Simplify the expression $$\displaystyle{y}-{5}{y}$$ by combining the like terms.
c) Simolify the expression $$\displaystyle{3}{x}^{{{2}}}+{5}{x}^{{{2}}}-{2}$$ by combining the like terms.

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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 $$\displaystyle{8}{x}^{{{2}}}-{2}$$