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# Algebra 1 - Monomials

## Introduction

• An algebraic expression that has a single term is called Monomials.
• 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

• ${x}^{3}·{x}^{5}={x}^{3+5}={x}^{8}$
• $2{a}^{2}b·3a{b}^{4}=6{a}^{2+1}{b}^{1+4}=6{a}^{3}{b}^{5}$
• $\frac{{a}^{5}}{{a}^{2}}={a}^{5-2}={a}^{3}$
• $\frac{12{a}^{3}{b}^{6}{c}^{2}}{-3a{b}^{2}c}=-4{a}^{3-1}{b}^{6-2}{c}^{2-1}=-4{a}^{2}{b}^{4}c$

## 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.
• can't be added as the terms/variables are different.