Expanding and Simplifying the Expression: 3x(x+1)^2 - 5x^2(x+1) + 7(x+1)
In this article, we will explore the process of expanding and simplifying the algebraic expression: 3x(x+1)^2 - 5x^2(x+1) + 7(x+1).
Expanding the Expression
To expand the expression, we need to follow the order of operations (PEMDAS) and evaluate the expressions inside the parentheses first.
Expanding (x+1)^2
(x+1)^2 can be expanded using the formula: (a+b)^2 = a^2 + 2ab + b^2
(x+1)^2 = x^2 + 2x + 1
Expanding the Expression
Now, let's expand the entire expression:
3x(x+1)^2 = 3x(x^2 + 2x + 1) = 3x^3 + 6x^2 + 3x
-5x^2(x+1) = -5x^3 - 5x^2
7(x+1) = 7x + 7
Combining Like Terms
Now, let's combine like terms:
3x^3 + 6x^2 + 3x - 5x^3 - 5x^2 + 7x + 7
Combine the x^3 terms: 3x^3 - 5x^3 = -2x^3
Combine the x^2 terms: 6x^2 - 5x^2 = x^2
Combine the x terms: 3x + 7x = 10x
The simplified expression is:
-2x^3 + x^2 + 10x + 7
Conclusion
In this article, we have successfully expanded and simplified the expression: 3x(x+1)^2 - 5x^2(x+1) + 7(x+1). The final simplified expression is -2x^3 + x^2 + 10x + 7.
