Combining Like Terms

04.39

Diposting oleh Melany Christy

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

Numbers: Constant, known quantities that remain fixed.
Examples: 100, 23, -157, π, e

Variables: Symbols that represent unknown quantities.
Examples: θ, x, y, and any other letter of the alphabet

Exponents: A known or unknown quantity that raises a base to a given power.
Examples: x² (the 2 is the exponent, x is the base); ab^x(the x is the exponent, b is the base); e^u (the u is the exponent)

Each monomial has a coefficient, which is the number that is multiplied by the other elements of the term.
Quick tip for finding the coefficient: It’s usually the number at the beginning of the monomial.

Examples of Monomials

15xyz
Coefficient: 15
-b²
Coefficient: -1 because -b² is the same as -1b²
21pq³
Coefficient: 21
4ac
Coefficient: 4

When monomials, or terms, share the same variable and same exponent, they are like terms. Note: Like terms don't have to share the same coefficient.

Like Terms Practice #1

Find the like terms in the following expression:

x + 2y + 3y + 3x + 15y

Answers:
x and 3x are like terms.
2y, 3y, and 15y are like terms.

Like Terms Practice #2

Find the like terms in the following expression:

x + -x²+ - x³+ y² - y + 4y⁴

None of these terms are alike because of different variables and exponents.