(x%5E2-5x%2B25)-(x%2B3)%5E3x-2)(x%5E2%2B2x%2B4)-(x-1)%5E3.jpeg "(x+5)(x^2-5x+25)-(x+3)^3x-2)(x^2+2x+4)-(x-1)^3")
** Expansion and Simplification of Algebraic Expressions **
In this article, we will discuss the expansion and simplification of algebraic expressions. We will use the following expression as an example:
$(x+5)(x^2-5x+25)-(x+3)^3x-2)(x^2+2x+4)-(x-1)^3$
** Step 1: Expand the Expressions **
Let's start by expanding the expressions:
$(x+5)(x^2-5x+25) = x^3 - 5x^2 + 25x + 5x^2 - 25x + 125$
$= x^3 + 125$
$(x+3)^3 = x^3 + 9x^2 + 27x + 27$
$x-2)(x^2+2x+4) = x^3 + 2x^2 + 4x - 2x^2 - 4x - 8$
$= x^3 - 2x - 8$
$(x-1)^3 = x^3 - 3x^2 + 3x - 1$
** Step 2: Simplify the Expressions **
Now, let's simplify the expressions:
$(x+5)(x^2-5x+25) - (x+3)^3x - 2)(x^2+2x+4) - (x-1)^3$
$= x^3 + 125 - (x^3 + 9x^2 + 27x + 27)x - (x^3 - 2x - 8) - (x^3 - 3x^2 + 3x - 1)$
** Step 3: Combine Like Terms **
Now, let's combine like terms:
$= x^3 + 125 - x^4 - 9x^3 - 27x^2 - 27x - x^3 + 2x + 8 - x^3 + 3x^2 - 3x + 1$
$= -x^4 - 7x^3 - 24x^2 - 20x + 134$
And that's the final simplified expression!
** Conclusion **
In this article, we have successfully expanded and simplified the given algebraic expression. We hope this example has helped you understand the process of expanding and simplifying algebraic expressions.
