Solving the Equation: (x+4)(x^24x+16)x(x5)(x+5)=264
This article will guide you through solving the algebraic equation: (x+4)(x^24x+16)x(x5)(x+5)=264. We'll break down the steps involved in simplifying the equation and ultimately finding the solution(s) for x.
Expanding and Simplifying the Equation

Expand the first set of parentheses:
The expression (x+4)(x^24x+16) represents the expansion of a sum of cubes. We can use the formula: (a+b)(a^2ab+b^2) = a^3 + b^3.
Therefore, (x+4)(x^24x+16) = x^3 + 4^3 = x^3 + 64

Expand the second set of parentheses:
The expression x(x5)(x+5) involves the difference of squares formula: (ab)(a+b) = a^2  b^2.
Therefore, x(x5)(x+5) = x(x^2  25) = x^3  25x

Substitute the expanded expressions back into the original equation:
The equation now becomes: x^3 + 64  (x^3  25x) = 264

Simplify by distributing the negative sign:
x^3 + 64  x^3 + 25x = 264

Combine like terms:
25x + 64 = 264
Solving for x

Isolate the x term:
25x = 200

Divide both sides by 25:
x = 8
Solution
The solution to the equation (x+4)(x^24x+16)x(x5)(x+5)=264 is x = 8.