Algebra 1 - Monomials

Introduction

An algebraic expression that has a single term is called Monomials.
$2, 3 x y, 4 a^{2} b, and 52 m^{2} n^{3}$ 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.

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.

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.

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

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.

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