(x-1)^3+(2-x)(4+2x+x^2)+3x(x+2)=17

2 min read Jun 17, 2024

Solving the Equation (x-1)^3 + (2-x)(4+2x+x^2) + 3x(x+2) = 17

This article will guide you through the process of solving the given equation:

(x-1)^3 + (2-x)(4+2x+x^2) + 3x(x+2) = 17

1. Expand the Expressions:

Begin by expanding the expressions on the left side of the equation.

(x-1)^3: Using the binomial theorem or by multiplying (x-1) by itself three times, we get: (x-1)^3 = x^3 - 3x^2 + 3x - 1
(2-x)(4+2x+x^2): This is a product of a difference of squares and a perfect square trinomial. Using the appropriate formulas, we get: (2-x)(4+2x+x^2) = 8 - x^3
3x(x+2): This is a simple multiplication: 3x(x+2) = 3x^2 + 6x

2. Combine Like Terms:

Now, substitute these expanded expressions back into the original equation and combine like terms:

x^3 - 3x^2 + 3x - 1 + 8 - x^3 + 3x^2 + 6x = 17

Simplifying, we get:

9x + 7 = 17

3. Solve for x:

Subtract 7 from both sides:

9x = 10

Divide both sides by 9:

x = 10/9

Solution:

Therefore, the solution to the equation (x-1)^3 + (2-x)(4+2x+x^2) + 3x(x+2) = 17 is x = 10/9.