(x-2)(x-3)-simplify.jpeg "(x-1)(x-2)(x-3) Simplify")
Simplifying the Expression: (x-1)(x-2)(x-3)
In algebra, simplifying expressions is an essential skill to master. One such expression that we will focus on in this article is (x-1)(x-2)(x-3). Let's break it down step by step to simplify it.
Expanding the Expression
To simplify the expression, we need to expand it first. We will use the distributive property of multiplication over subtraction to expand each term.
(x-1)(x-2) = x^2 - 3x + 2
Now, we will multiply the resulting expression with (x-3):
(x^2 - 3x + 2)(x-3) = ?
Expanding further...
Using the distributive property again, we get:
= x^3 - 3x^2 + 2x - 3x^2 + 9x - 6
Combining Like Terms
We can combine like terms to simplify the expression further:
= x^3 - 6x^2 + 11x - 6
And that's it! We have successfully simplified the expression (x-1)(x-2)(x-3).
Final Answer
(x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x - 6
Remember to always follow the order of operations (PEMDAS) and to combine like terms when simplifying expressions. With practice, you'll become proficient in simplifying even the most complex expressions!
