Monomials

Introduction to monomials

In Algebra, a monomial or a term is comprised of a combination of the following: numbers, variables, and exponents. In Algebraic expressions and equations, terms or monomials are separated by addition and subtraction signs

Monomial is an algebraic expression with only one term.

For example, 7xy, - 5m, 3z², 4 etc.

It contains a constant and variables. We use letters x, y, l, m, ... etc. to denote variables. A variable can take various values. Its value is not fixed. On the other hand, a constant has a fixed value. Examples of constants are: 4, 100, - 17, etc.

1. 15xy
Coefficient: 15 , variables x and y and exponent 1

2. -2ab2
Coefficient: -2 , variables are a and b and exponent is 2

3. 41pq3
Coefficient: 41 , variables are p and q and exponent is 3

4. -a2
Coefficient: -1 because -a2 is the same as -1a2

Variable is a and the exponent is 2

When terms or monomials contain the same variable and same exponent, they are like terms.

Addition and subtraction of monomials is done by combining the like terms.

Simplify the following expressions.

1) 7 + 7x +13x

2) -12c + 12c

3) 8y - 3y

4) x² + y² + x

5) 4np³ - 8np³

Answers :

1) 20x + 7

2) 0

3) 5y

4) x² + y² + x

5) -4np³

When we multiply the monomial, first step is multiplying the numerical coefficients (for e.g. 4 and the 8) and then multiplying the literal coefficients or variables (a and b). Next step is to multiply the like variables by adding their exponents (for e.g. 3+2). (Rule am * an = am+n).

Simplify the following monomials:

1) 5 ab * 5 b

2) 2 xy * 3 yz

3) -4 x⁶ * 6x²

4) 4 b⁵c * 7 ab²c

5) 20 ac * pq

Answers :

1) 25 ab²

2) 6 xy²z

3) -24 x⁸

4) 28 ab⁷c²

5) 20acpq

When we divide the monomial, first step is dividing the numerical coefficients (for e.g. 24 and 8) and then dividing the literal coefficients or variables(a and b). Next step is to divide the like variables by subtracting their exponents (for e. g. 5-2 ). (Rule $\frac{am}{an}$ = am-n).

Simplify the following monomials:

1) $\frac{25 ab}{5 b}$

2) $\frac{15 ab^4 c}{3 bc}$

3) $\frac{-24 x^6}{6x^2}$

4) $\frac{49 a^2 b^5 c}{7 ab^2 c}$

5) $\frac{20 ac}{ac}$

Answers:

1) 5 a

2) 5 ab³

3) -4 x⁴

4) 7 ab³

5) 20