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Find the product of (x^2+2x+1)(x^2-1)

User Europa
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Final answer:

The product of the polynomials (x^2+2x+1) and (x^2-1) is calculated by distributing each term of the first polynomial by each term of the second, resulting in a simplified final product of x^4 + 2x^3 - x^2 - 2x - 1.

Step-by-step explanation:

The student has been asked to find the product of the polynomials (x^2+2x+1) and (x^2-1). Multiplying polynomials involves distributing each term in the first polynomial by each term in the second polynomial.

Step by step, the multiplication looks like this:

  • x^2 × x^2 = x^4
  • x^2 × (-1) = -x^2
  • 2x × x^2 = 2x^3
  • 2x × (-1) = -2x
  • 1 × x^2 = x^2
  • 1 × (-1) = -1

Now, we combine like terms:

  • x^4
  • -x^2 + 2x^3
  • x^2 - 2x
  • -1

When simplified, the final product is:

x^4 + 2x^3 - x^2 - 2x - 1

User Ravi Ram
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