(x%2B2)(x%2B3)-expand-and-simplify.jpeg "(x+1)(x+2)(x+3) Expand And Simplify")
Expanding and Simplifying (x+1)(x+2)(x+3)
In this article, we will explore the process of expanding and simplifying the expression (x+1)(x+2)(x+3). This expression is a product of three binomials, and we will use the distributive property of multiplication over addition to expand it.
Expanding the Expression
To expand the expression (x+1)(x+2)(x+3), we need to multiply each term in the first binomial (x+1) by each term in the second binomial (x+2), and then multiply the result by each term in the third binomial (x+3).
Let's start by multiplying the first two binomials:
(x+1)(x+2) = x(x+2) + 1(x+2)
= x^2 + 2x + x + 2
= x^2 + 3x + 2
Now, we multiply the result by the third binomial (x+3):
(x^2 + 3x + 2)(x+3) = x^2(x+3) + 3x(x+3) + 2(x+3)
= x^3 + 3x^2 + 3x^2 + 9x + 2x + 6
= x^3 + 6x^2 + 11x + 6
Simplifying the Expression
The expanded expression x^3 + 6x^2 + 11x + 6 is already in its simplest form. There are no like terms to combine, and no common factors to factor out.
Therefore, the final answer is:
(x+1)(x+2)(x+3) = x^3 + 6x^2 + 11x + 6
In conclusion, we have successfully expanded and simplified the expression (x+1)(x+2)(x+3) using the distributive property of multiplication over addition. The result is a cubic expression with no like terms or common factors.
