# What is expression decoding? (with examples) - science - 2023

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**Decoding mathematical expressions****Decoding simple math expressions****Decoding algebraic expressions****Decoding polynomials****References**

The **expression decoding** refers to the way of verbally expressing a mathematical expression. In math, a **expression**, also called a mathematical expression, is a combination of coefficients and literal parts joined through other mathematical signs (+, -, x, ±, /, [],), to form a mathematical operation.

In simpler words, the coefficients are represented by numbers, while the literal part is made up of letters (generally the last three letters of the alphabet, a, b and c, are used to designate the literal part).

In turn, these "letters" represent quantities, variables, and constants that can be assigned a numerical value.

Mathematical expressions are made up of terms, which are each of the elements that are separated by operation symbols. For example, the following mathematical expression has four terms:

5x^{2} + 10x + 2x + 4

It should be noted that expressions can be constituted only by coefficients, by coefficients and literal parts and only by literal parts.

For example:

25 + 12

2x + 2y (algebraic expression)

3x + 4 / y + 3 (irrational algebraic expression)

x + y (integer algebraic expression)

4x + 2y^{2} (integer algebraic expression)

**Decoding mathematical expressions**

**Decoding simple math expressions**

1. a + b: The sum of two numbers

For example: 2 + 2: The sum of two and two

2. a + b + c: The sum of three numbers

For example: 1 + 2 + 3: The sum of one, two and three

3. a - b: The subtraction (or difference) of two numbers

For example: 2 - 2: The subtraction (or difference) of two and two

4. a x b: The product of two numbers

For example: 2 x 2: The product of two and two

5. a **÷** b: The quotient of two numbers

For example: 2/2: The quotient of two and two

6. 2 (x): Double a number

For example: 2 (23): Double 23

7. 3 (x): Triple a number

For example: 3 (23): Triple 23

8. 2 (a + b): Double the sum of two numbers

For example: 2 (5 + 3): Double the sum of five and three

9. 3 (a + b + c): Triple the sum of three numbers

For example: 3 (1 + 2 + 3): Triple the sum of one, two and three

10. 2 (a - b): Double the difference of two numbers

For example: 2 (1 - 2): Double the difference of one and two

11. x / 2: Half of a number

For example: 4/2: Half of four

12. 2n + x: The sum of twice a number and another number

For example: 2 (3) + 5: The sum of the double of three and five

13. x> y: “X” is greater than “ye”

For example: 3> 1: Three is greater than one

14. x <y: “X” is less than “ye”

For example: 1 <3: One is less than three

15. x = y: "X" is equal to "ye"

For example: 2 x 2 = 4: The product of two and two is equal to four

16. x^{2 }: The square of a number or a number squared

For example: 5^{2 }: The square of five or five squared

17. x^{3 }: The cube of a number or a number cubed

For example: 5^{3} : The cube of five or five cubed

18. (a + b) ^{2} : The square of the sum of two numbers

For example: (1 + 2) ^{2} : The square of the sum of one and two

19. (x - y) / 2: Half the difference of two numbers

For example: (2 - 5) / 2: Half the difference of two and five

20. 3 (x + y) ^{2} : Triple the square of the sum of two numbers

For example: 3 (2 + 5) ^{2 }: Triple the block of the sum of two and five

21. (a + b) / 2: The semi-sum of two numbers

For example: (2 + 5) / 2: The semi-sum of two and five

**Decoding algebraic expressions**

- 2 x
^{5}+ 7 / and + 9: [Two X's raised to five] plus [seven over ye] plus [nine]

- 9 x + 7y + 3 x
^{6}- 8 x^{3}+ 4 and: [Nine Xs] plus [seven and e] plus [three X to the sixth] minus [eight X to the 3] plus [four ye]

- 2x + 2y: [Two Xs] plus [Two Ye]

- x / 2 - y
^{5}+ 4y^{5}+ 2x^{2}: [x over 2] minus [ye raised to five] plus [four ye raised to five] plus [two x's squared]

- 5/2 x + y
^{2 }+ x: [Five over two x's] plus [ye squared] plus [x's]

**Decoding polynomials**

- 2x
^{4}+ 3x^{3}+ 5x^{2}+ 8x + 3: [Two of Xs to four] plus [three of Xs to three] plus [five of Xs squared] plus three

- 13y
^{6}+ 7y^{4 }+ 9y^{3}+ 5y: [Thirteen of ye raised to six] plus [seven of ye raised to four] plus nine of ye raised to three] plus [five of ye]

- 12z8 - 5z6 + 7z5 + z4 - 4z3 + 3z2 + 9z: [Twelve zeta to eight] minus [five zeta to six] plus [seven zeta to five] plus [zeta to four ] minus [four zeta squared] plus [three zeta squared] plus [nine zeta]

**References**

- Wrinting expressions with variables. Retrieved on June 27, 2017, from khanacademy.org.
- Algebraic expressions. Retrieved on June 27, 2017, from khanacademy.org.
- Comprehension of algebraic expressions by experienced users of mathematics. Retrieved on June 27, 2017, from ncbi.nlm.nih.gov.
- Writing mathematical expressions. Retrieved on June 27, 2017, from mathgoodies.com.
- Teaching arithmetic and algebraic expressions. Retrieved on June 27, 2017, from emis.de.
- Expressions (mathematics). Retrieved on June 27, 2017, from en.wikipedia.org.
- Algebraic expressions. Retrieved on June 27, 2017, from en.wikipedia.org.