Example of Algebraic Expressions

The algebraic expressions are relationships between variables and constants, what indicate an operation between them. Each part of this relationship, separated by an addition (+) or subtraction (-) sign, is called finished. A term can be formed by four main elements:

1. Sign (+, -), which says if it is positive or negative.
2. Literal: letter assigned to the variable.
3. Coefficient: number that tells how many times that expression is multiplied.
4. Grade: is the exponent to which a literal is raised.

Types of algebraic expressions

• Monomials: have only one term (πr²), (4x²).
• Binomials: have two terms (2x³ + x²), (x² + x).
• Trinomials: have three terms. (x² + 2x + 1), (4x² + 4x + 1).
• Polynomials: they have 4 terms upwards (x⁴ + x³ + 3x² + 2x + 2).

Algebraic expressions and equations

Among the infinite algebraic expressions are those that represent a specific operation, and that helps a science to solve a problem. For example, in geometry, to calculate the area of ​​a circle, the algebraic expression is used:

πr²

That as a verbal proposition it is said: "The product of Pi by the radius squared". As it is used to calculate and know the value of the area, it is then written:

A = πr²

And finally it reads: "The area of ​​a circle is equal to the product of Pi times the radius squared." This equality, in which we have algebraic expressions, is called algebraic equation. And when it is used to solve so many problems (calculate areas of all circles), it is also named formula.

• Read more about how at: Algebraic language.

Examples of algebraic expressions

Examples of each type of algebraic expression

Monomials

• 4x²
• 3x
• 6y³
• 2w
• xy²z
• 4fg
• 8m³not²
• p²qr⁵s
• 6th²b²c²
• 10d³F²j²

• More information in: Monomials.

Binomials

• a + b
• 2 C² - d
• 4fg + 2gh
• 2x²yz - 4xy
• x - y²
• r² + 4r
• 7u³ + 4u²
• 9y³ + 3y²
• 2m + 4n
• 3j² + 4jkl

• More information in: Binomials.

Trinomials

• x² + 2x + 1
• 4x² + 8x + 2
• x³ + x² + x
• to² + b² + c²
• ax² - bx² - cx²
• 4m² + 4mn - 3n²
• 2j²k² + 3j²k - 4jk²
• 3rd²b + 3ab⁴ - 3abc²
• abc + a²b²c + abc²
• 7mn + 4mn² - 3m²n

• More information in: Trinomials.

Polynomials

• a + b + c + d + e
• a - b - c - d + e
• to² + b³ - c⁴ + d⁵
• 2fg + 3gh - 4fh + 2gj
• 4x + 3xy + 2xyz - 3yz
• 10x²y + 3xy² - 4x²Y² + xy
• 9ab + 10a²b - 8ab² + 4a²b²
• a + b - c + d - e + f - g + h - j
• v + w - x + y - z
• jk + lm - no + p³what³ - rs + t²or²v

• More information in: Polynomials.