Question

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

Answer 1

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