# Question Video: Simplifying Expressions Involving Factorials Mathematics

Simplify (π + 2)!/π!.

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### Video Transcript

Simplify π plus two factorial divided by π factorial.

We recall that π factorial is equal to π multiplied by π minus one multiplied by π minus two all the way down to one. We need to multiply all of the integers or whole numbers from our number down to one. In order to calculate π plus two factorial, we would need to multiply π plus two by π plus one by π by π minus one by π minus two all the way down to one.

We notice that from π onwards is equal to π factorial. π plus two factorial is therefore equal to π plus two multiplied by π plus one multiplied by π factorial. If we substitute this into our question, we have π plus two multiplied by π plus one multiplied by π factorial all divided by π factorial. Any number divided by itself is equal to one. Therefore, π factorial divided by π factorial is one. We are therefore left with π plus two multiplied by π plus one.

Whilst we could distribute the parentheses or expand the brackets here, we donβt need to, as the expression is already in its simplest form. The simplified version of π plus two factorial divided by π factorial is π plus two multiplied by π plus one.