Expansion of (x+1)(x+2)(x+3)
In algebra, expanding a product of binomials can be a challenging task, especially when dealing with multiple factors. In this article, we will explore the expansion of the product (x+1)(x+2)(x+3)
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Step 1: Expand the first two factors
To start, let's expand the first two factors:
(x+1)(x+2) = x^2 + 3x + 2
This is a simple expansion, where we multiply each term in the first factor by each term in the second factor.
Step 2: Expand the result with the third factor
Now, let's expand the result with the third factor:
(x^2 + 3x + 2)(x+3) = ?
To do this, we'll multiply each term in the first factor by each term in the third factor:
x^2
multiplied byx+3
givesx^3 + 3x^2
3x
multiplied byx+3
gives3x^2 + 9x
2
multiplied byx+3
gives2x + 6
Now, let's combine like terms:
x^3 + 3x^2 + 3x^2 + 9x + 2x + 6
Simplifying the expression
Finally, let's simplify the expression by combining like terms:
= x^3 + 6x^2 + 11x + 6
And that's it! We have successfully expanded the product (x+1)(x+2)(x+3)
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Final answer
The final answer is:
(x+1)(x+2)(x+3) = x^3 + 6x^2 + 11x + 6