Define a variable and write an algebraic expression for each phrase.

the diffrence of 8 and a number

the product of 2 and a number

Let x be the variable, then

8-x
and
2*x

how add positive and negative numbers

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To define a variable and write an algebraic expression, you can follow these steps:

1. Choose a variable to represent the unknown quantity. Common variables used in algebra include "x," "y," and "n." For clarity, let's use "x" in this case.

2. Translate the English phrase into a mathematical expression using the chosen variable. Here are the translations for the given phrases:

- The difference of 8 and a number:
To express the difference, we subtract the number from 8. Since the number is represented by the variable "x," the algebraic expression would be:
8 - x

- The product of 2 and a number:
To express the product, we multiply 2 by the number. Using the variable "x," the algebraic expression would be:
2 * x

Remember, the key is to understand the phrasing and then use algebraic operations to represent the relationship between the given quantities.