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(x+1)^3-(x-4)(x+4)-x^3

2 min read Jun 16, 2024
(x+1)^3-(x-4)(x+4)-x^3

Simplifying the Expression: (x+1)^3 - (x-4)(x+4) - x^3

This article will guide you through the process of simplifying the algebraic expression: (x+1)^3 - (x-4)(x+4) - x^3.

Expanding and Simplifying

  1. 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

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

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

  4. 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 - (x-4)(x+4) - x^3 to its simplest form, 2x^2 + 3x + 17.

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