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A factorial is a special mathematical operation denoted by the symbol '!'. When you see a number followed by '!', it means you need to multiply that number by every positive integer less than it.
For example, if you want to find 5!, you would calculate:
\( 5! = 5 \times 4 \times 3 \times 2 \times 1 \).
It's helpful to think of factorials as building blocks that decrease step by step.
Factorials are often used in algebra, calculus, and for counting permutations or combinations.
The factorial of zero (0!) is defined to be 1 by convention.
For smaller numbers, you can compute it manually, but for larger numbers, it's often easier to use a calculator or computer.

Multiplication in algebra works the same way as multiplication with regular numbers, but often involves variables and coefficients. When multiplying numbers, you combine them to get a larger product. For instance:
If you multiply 4 by 5, you get 20.
Now, considering our example expression \(6! \times 7\), after we calculate \(6!\), which is 720, we multiply it by 7:
\(720 \times 7 = 5040\).
Understanding how to multiply these numbers correctly is crucial. A small mistake in multiplication can lead to a completely wrong answer, so it's important to double-check your work.
When dealing with variables, it's a bit different. For example:
\(3a \times 4b = 12ab\).
Just remember to multiply the numbers (coefficients) and then combine the letters (variables).

Evaluating expressions means finding the value of an algebraic or numerical expression.
It often involves combining operations like addition, subtraction, multiplication, and division.
To evaluate the expression \(6! \times 7\), follow these steps:

• First, compute the factorial (6!).
• Second, multiply the result by the number 7.
• Finally, write down your answer and ensure every calculation is correct.

Breaking the problem into smaller steps can make it easier to manage and understand. Ensure you follow the correct order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Using tools such as calculators can help verify your result, but understanding the underlying process is essential.