Solving the Equation (x+2)(x2)(x+1)^2=7
This article will guide you through the process of solving the equation (x+2)(x2)(x+1)^2=7. We will use algebraic manipulation to isolate the variable x and find its solution(s).
Simplifying the Equation

Expand the products:
 (x+2)(x2) is a difference of squares: (x+2)(x2) = x²  4
 (x+1)² is a perfect square: (x+1)² = x² + 2x + 1

Substitute the expanded expressions back into the original equation: x²  4  (x² + 2x + 1) = 7

Simplify by distributing the negative sign: x²  4  x²  2x  1 = 7

Combine like terms: 2x  5 = 7
Solving for x

Isolate the x term: 2x = 12

Divide both sides by 2: x = 6
Conclusion
Therefore, the solution to the equation (x+2)(x2)(x+1)^2=7 is x = 6.