Polynomial Multiplication Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Expand (x+1)2(x−1)(x + 1)^2(x - 1).

Solution

  1. 1
    First: (x+1)2=x2+2x+1(x+1)^2 = x^2 + 2x + 1.
  2. 2
    Then: (x2+2x+1)(x−1)=x3−x2+2x2−2x+x−1=x3+x2−x−1(x^2 + 2x + 1)(x - 1) = x^3 - x^2 + 2x^2 - 2x + x - 1 = x^3 + x^2 - x - 1.

Answer

x3+x2−x−1x^3 + x^2 - x - 1
Complex products can be broken into steps: first expand one pair, then multiply the result by the remaining factor. This avoids errors from trying to handle all terms at once.

About Polynomial Multiplication

Multiplying polynomials by distributing every term in one polynomial to every term in the other, then combining like terms.

Learn more about Polynomial Multiplication →

More Polynomial Multiplication Examples

Example 1 easy

Multiply [formula] using FOIL.

Example 2 medium

Expand [formula].

Example 3 easy

Multiply [formula].

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