Simplifying the Expression: (x+1)^3  (x4)(x+4)  x^3
This article will guide you through the process of simplifying the algebraic expression: (x+1)^3  (x4)(x+4)  x^3.
Expanding and Simplifying

Expand (x+1)^3: This involves using the binomial theorem or simply multiplying (x+1) by itself three times. (x+1)^3 = (x+1)(x+1)(x+1) = x^3 + 3x^2 + 3x + 1

Expand (x4)(x+4): This is a special case of the "difference of squares" pattern: (ab)(a+b) = a^2  b^2. (x4)(x+4) = x^2  16

Substitute the expanded terms back into the original expression: (x+1)^3  (x4)(x+4)  x^3 = (x^3 + 3x^2 + 3x + 1)  (x^2  16)  x^3

Simplify by removing parentheses and combining like terms: x^3 + 3x^2 + 3x + 1  x^2 + 16  x^3 = 2x^2 + 3x + 17
Conclusion
By expanding the terms and simplifying, we have successfully reduced the complex expression (x+1)^3  (x4)(x+4)  x^3 to its simplest form, 2x^2 + 3x + 17.