(x%2B2)(x%2B3)(x%2B6)-3x%5E2.jpeg "(x+1)(x+2)(x+3)(x+6)-3x^2")
Factoring and Simplifying the Expression (x+1)(x+2)(x+3)(x+6) - 3x^2
This article explores the process of factoring and simplifying the expression (x+1)(x+2)(x+3)(x+6) - 3x^2.
Expanding the Expression
First, let's expand the product of the four binomials:
(x+1)(x+2)(x+3)(x+6) = (x^2 + 3x + 2)(x^2 + 9x + 18)
Expanding this further results in:
x^4 + 12x^3 + 47x^2 + 72x + 36
Now, we can substitute this back into the original expression:
(x+1)(x+2)(x+3)(x+6) - 3x^2 = x^4 + 12x^3 + 47x^2 + 72x + 36 - 3x^2
Simplifying the Expression
Combining the like terms, we obtain:
x^4 + 12x^3 + 44x^2 + 72x + 36
Factoring the Simplified Expression
Unfortunately, this expression cannot be factored further using simple methods like grouping or difference of squares. However, we can attempt to find its roots using numerical methods or graphing tools.
Conclusion
In conclusion, the expression (x+1)(x+2)(x+3)(x+6) - 3x^2 can be simplified to x^4 + 12x^3 + 44x^2 + 72x + 36. While this simplified expression cannot be factored easily, it can be further analyzed using numerical or graphical methods to determine its roots and behavior.