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In algebra, variables play a crucial role. Variables are symbols used to represent unknown values or quantities that can change. Typically, letters such as 'a', 'b', 'x', or 'y' are used as variables.

For example, in the exercise, the variables are 'a' and 'b'. These variables stand in for numbers that we don't know yet. Learning how to use variables is the first step towards understanding algebraic expressions. Recognizing and correctly identifying variables in any given problem is essential, as it sets up the foundation for solving the expression.

Addition in algebra works similarly to regular addition, but it involves variables. When the problem mentions 'the sum of a and b', it means you need to add the variables 'a' and 'b' together. This can be written as:
\[a + b\]

It's important to understand that the sum of two variables combines them into a single expression. No calculations are needed at this point because we don't know the values for 'a' and 'b'. Instead, we simply write them together with a plus sign in between.

Remember, understanding algebraic addition is as simple as recognizing that you're combining quantities. As we often deal with unknowns, handling variables becomes second nature with practice.

Multiplication in algebra is also straightforward but has its own rules. When an expression is said to be 'twice' or multiplied by 2, you multiply the entire expression by 2. In this exercise, after identifying and adding the variables (\[a + b\]), you are instructed to take 'twice' their sum. This means:
\[2 \times (a + b)\]

When writing algebraic expressions, we use parentheses to indicate that the entire sum should be multiplied by 2. This ensures clarity, showing that both 'a' and 'b' should be added first before multiplying the result by 2.

Multiplication in algebra helps in scaling expressions. It shows how variables and their sums can be adjusted by factors, which is key to manipulating algebraic equations effectively.