## Introduction

- An algebraic expression that has a single term is called Monomials.
- $2,3xy,4{a}^{2}b,\text{and}52{m}^{2}{n}^{3}$ are some examples of Monomials.
- In 3xy, the number 3 is called a coefficient.
- To add or subtract the monomials, perform the operation on the coefficients and keep the variable and exponents the same.
- The same rules that apply to the addition and subtraction of signed numbers apply to monomials as well.

## Adding & Subtracting Monomials

- To add or subtract the monomials, perform the operation on the coefficients and keep the variable and exponents the same.
- The same rules that apply to the addition and subtraction of signed numbers apply to monomials as well.

## Multiplying and Dividing Monomials

- To multiply a monomial by a monomial, multiply the numerical coefficient and add the exponents of the same bases.
- To divide one monomial with another, divide the numerical coefficient and subtract the exponent of the denominator (divisor) from the exponent of the numerator (dividend).
- The sign number rules apply to monomial multiplications and divisions.
- Check out the Laws of Exponents rules to learn how to raise a monomial to a power.

## Solved Examples

- $4x+5x=9x$
- $3{x}^{2}+5{x}^{2}=7{x}^{2}$
- $4m{n}^{3}+3m{n}^{3}=7m{n}^{3}$
- $7x-3x=4x$
- $5{x}^{2}+2{x}^{2}=3{x}^{2}$
- $-7{a}^{2}+2{a}^{2}+3{a}^{2}=-2{a}^{2}$
- $4ab+3ab-2ab-(-3ab)=8ab$
- $\left({a}^{2}\right)\left({a}^{4}\right)={a}^{2+4}={a}^{6}$
- ${x}^{3}\xb7{x}^{5}={x}^{3+5}={x}^{8}$
- $2{a}^{2}b\xb73a{b}^{4}=6{a}^{2+1}{b}^{1+4}=6{a}^{3}{b}^{5}$
- $\frac{{a}^{5}}{{a}^{2}}={a}^{5-2}={a}^{3}$
- $\frac{12{a}^{3}{b}^{6}{c}^{2}}{-3a{b}^{2}c}=-4{a}^{3-1}{b}^{6-2}{c}^{2-1}=-4{a}^{2}{b}^{4}c$

## Cheat Sheet

- Monomials can be added or subtracted only when the terms are alike.
- The same rules that apply to the addition and subtraction of signed numbers apply to monomials.

## Blunder Areas

- Only monomials with the same variable and exponents (if any) can be added or subtracted.
- $4ab+4xy$can't be added as the terms/variables are different.

- Rishi Jethwa
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