(3x%5E2%2Bx)-(6x%2B3)(x%5E2-2x).jpeg "(2x-1)(3x^2+x)-(6x+3)(x^2-2x)")
Simplifying the Expression: (2x-1)(3x^2+x)-(6x+3)(x^2-2x)
This article will guide you through simplifying the given algebraic expression: (2x-1)(3x^2+x)-(6x+3)(x^2-2x). We will utilize the distributive property and then combine like terms to reach a simplified form.
Step 1: Expanding the Products
We need to expand the products using the distributive property (also known as FOIL method).
(2x-1)(3x^2+x) = (2x * 3x^2) + (2x * x) + (-1 * 3x^2) + (-1 * x) = 6x^3 + 2x^2 - 3x^2 - x
(6x+3)(x^2-2x) = (6x * x^2) + (6x * -2x) + (3 * x^2) + (3 * -2x) = 6x^3 - 12x^2 + 3x^2 - 6x
Step 2: Combining Like Terms
Now, we have the expanded form of the expression:
(6x^3 + 2x^2 - 3x^2 - x) - (6x^3 - 12x^2 + 3x^2 - 6x)
Let's combine the terms with the same powers of 'x':
- x^3 terms: 6x^3 - 6x^3 = 0
- x^2 terms: 2x^2 - 3x^2 + 12x^2 - 3x^2 = 8x^2
- x terms: -x + 6x = 5x
Step 3: The Simplified Expression
After combining like terms, the simplified expression is:
8x^2 + 5x
Therefore, the simplified form of the given expression (2x-1)(3x^2+x)-(6x+3)(x^2-2x) is 8x^2 + 5x.