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(2x^3-1)(5x+2)-2x^2(5x^2+2x)=8

2 min read Jun 16, 2024
(2x^3-1)(5x+2)-2x^2(5x^2+2x)=8

Solving the Equation: (2x^3-1)(5x+2)-2x^2(5x^2+2x)=8

This article will guide you through the steps of solving the given equation.

Step 1: Expanding the Equation

First, we need to expand the equation by multiplying the terms:

  • (2x^3-1)(5x+2): Using the FOIL method, we get:
    • 2x^3 * 5x = 10x^4
    • 2x^3 * 2 = 4x^3
    • -1 * 5x = -5x
    • -1 * 2 = -2
  • -2x^2(5x^2+2x): We distribute -2x^2 to both terms:
    • -2x^2 * 5x^2 = -10x^4
    • -2x^2 * 2x = -4x^3

Now, our equation becomes: 10x^4 + 4x^3 - 5x - 2 - 10x^4 - 4x^3 = 8

Step 2: Simplifying the Equation

Notice that the terms 10x^4 and -10x^4 cancel each other out, and so do 4x^3 and -4x^3. This leaves us with:

-5x - 2 = 8

Step 3: Isolating the Variable (x)

To isolate x, we will:

  1. Add 2 to both sides: -5x - 2 + 2 = 8 + 2 -5x = 10

  2. Divide both sides by -5: -5x / -5 = 10 / -5 x = -2

Solution

Therefore, the solution to the equation (2x^3-1)(5x+2)-2x^2(5x^2+2x)=8 is x = -2.

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