(2x%5E2-5x%2B1)-(2x-1)(3x%5E2%2B7x-5).jpeg "(3x-4)(2x^2-5x+1)-(2x-1)(3x^2+7x-5)")
Simplifying the Expression: (3x-4)(2x^2-5x+1)-(2x-1)(3x^2+7x-5)
This article explores the simplification of the given algebraic expression: (3x-4)(2x^2-5x+1)-(2x-1)(3x^2+7x-5). We will use the distributive property and combine like terms to arrive at the simplified form.
Step 1: Expand the Products
First, we expand each of the products using the distributive property (also known as FOIL method):
(3x-4)(2x^2-5x+1) = 3x(2x^2-5x+1) - 4(2x^2-5x+1) = 6x^3 - 15x^2 + 3x - 8x^2 + 20x - 4
(2x-1)(3x^2+7x-5) = 2x(3x^2+7x-5) - 1(3x^2+7x-5) = 6x^3 + 14x^2 - 10x - 3x^2 - 7x + 5
Step 2: Combine Like Terms
Now, we combine like terms from both expansions:
(6x^3 - 15x^2 + 3x - 8x^2 + 20x - 4) - (6x^3 + 14x^2 - 10x - 3x^2 - 7x + 5)
= 6x^3 - 6x^3 - 15x^2 - 8x^2 + 14x^2 + 3x^2 + 3x + 20x + 10x + 7x - 4 - 5
Step 3: Simplify
Finally, we combine all the terms to arrive at the simplified form:
= -7x^2 + 40x - 9
Therefore, the simplified form of the expression (3x-4)(2x^2-5x+1)-(2x-1)(3x^2+7x-5) is -7x^2 + 40x - 9.