Monomial: Algebra and Terms
n 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 * 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); abx(the x is the exponent, b is the base); eu (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 1. 15xyz
Coefficient: 15 2. -b2
Coefficient: -1 because -b2 is the same as -1b2 3. 21pq3
Coefficient: 21 4. 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.
Combining Like Terms
When combining like terms, or adding and subtracting monomials, remember that the variables and exponents must be the same.
I love shopping at the grocery store in the summer because of the delectable fruit. Below is a depiction of how I tally the peaches and plums that I buy. * 6 peaches + 5 peaches = 11 peaches * 16 plums + 5 plums = 21 plums * 6 peaches + 5 plums = 6 peaches + 5 plums
Notice that 6 peaches plus 5 plums does not equal
Examples: 100, 23, -157, π * 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); abx(the x is the exponent, b is the base); eu (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 1. 15xyz
Coefficient: 15 2. -b2
Coefficient: -1 because -b2 is the same as -1b2 3. 21pq3
Coefficient: 21 4. 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.
Combining Like Terms
When combining like terms, or adding and subtracting monomials, remember that the variables and exponents must be the same.
I love shopping at the grocery store in the summer because of the delectable fruit. Below is a depiction of how I tally the peaches and plums that I buy. * 6 peaches + 5 peaches = 11 peaches * 16 plums + 5 plums = 21 plums * 6 peaches + 5 plums = 6 peaches + 5 plums
Notice that 6 peaches plus 5 plums does not equal