Question

(х+1)(х-1)(х⁴+х²+1)-(х²-1)³=​

Answer 1

Ответ:

3x⁴ - 3x²

Объяснение:

(х+1)(х-1)(х⁴+х²+1)-(х²-1)³=​ (x²- 1)( (x²)² - 2 * (x²) * 1 + 1 + 3x²) - (x²- 1)³ = (x²- 1)( (x² - 1)² + 3x²) - (x²- 1)³ = (x² - 1)³ + 3x²(x²- 1) - (x²- 1)³ = 3x²(x²- 1) = 3x⁴ - 3x²

Answer 2

Let's simplify the given expression step by step:

1. Expand the first term, which is a product of three binomials: (x+1)(x-1)(x⁴+x²+1).

   (x+1)(x-1)(x⁴+x²+1) = (x²-1)(x⁴+x²+1)

2. Now, let's multiply the two binomials (x²-1) and (x⁴+x²+1):

   (x²-1)(x⁴+x²+1) = x⁶ + x⁴ + x² - x⁴ - x² - 1

3. Simplify the terms that cancel out:

   x⁶ - 1

Now, let's simplify the second term, which is (x²-1)³:

1. Cube the binomial (x²-1):

   (x²-1)³ = (x²-1)(x²-1)(x²-1)

2. Multiply the first two binomials using the distributive property:

   (x²-1)(x²-1) = x⁴ - x² - x² + 1 = x⁴ - 2x² + 1

3. Now, multiply the result by the third binomial:

   (x⁴ - 2x² + 1)(x²-1) = x⁶ - 2x⁴ + x² - x² + 2x² - 1

4. Simplify the terms that cancel out:

   x⁶ - 2x⁴ + 2x² - 1

Now, let's subtract the second expression from the first:

(x⁶ - 1) - (x⁶ - 2x⁴ + 2x² - 1)

Now, subtract each term in the second expression from the corresponding term in the first expression:

x⁶ - 1 - x⁶ + 2x⁴ - 2x² + 1

Now, simplify the terms:

(x⁶ - x⁶) + (2x⁴ - 2x⁴) + (-2x² + 2x²) + (-1 + 1) = 0

So, the simplified expression is 0.