Question

Выпооните действия (х2+1)(х+1)(х-1)

Answer 1

(x²+1)(x+1)(x-1)=(x²+1)(x²-1)=x⁴-1

Answer 2

Multiplying the Polynomials

To multiply the given polynomials (x+2)(x+1)(x-1), we can use the distributive property to expand the expression.

Step 1: Expand the Expression

We can expand the expression by multiplying each term in the first polynomial by each term in the second polynomial, and then by the third polynomial.

Step 2: Perform the Multiplication

Let's perform the multiplication:

(x+2)(x+1)(x-1) = x(x+1)(x-1) + 2(x+1)(x-1)

Step 3: Continue the Expansion

Expanding further:

x(x+1)(x-1) = x(x^2 - x + x - 1) = x(x^2 - 1)

2(x+1)(x-1) = 2(x^2 - x + x - 1) = 2(x^2 - 1)

Step 4: Combine the Terms

Combining the terms:

x(x^2 - 1) + 2(x^2 - 1) = x^3 - x + 2x^2 - 2

Step 5: Simplify the Expression

Simplifying the expression:

x^3 - x + 2x^2 - 2

So, the result of multiplying the polynomials (x+2)(x+1)(x-1) is x^3 + 2x^2 - x - 2.