Question

14.29. 1) y = (x + 1)3 - (x + 2)3; 2) 4 = (2- 1)3- (2 - 2)8? 3) y = (x - 1)3 • (x - 2) - (x - 2)2 (x - 1).

Answer 1

Алгебра 8-класс

5-9 алгебра

формулы

Answer 2

Let's evaluate each of the given expressions one by one:

1. y = (x + 1)³ - (x + 2)³

To simplify this expression, we can expand the cubes using the binomial expansion formula:

(x + 1)³ = x³ + 3x² + 3x + 1 (x + 2)³ = x³ + 6x² + 12x + 8

Substituting these expanded forms back into the original expression:

y = (x³ + 3x² + 3x + 1) - (x³ + 6x² + 12x + 8) = x³ + 3x² + 3x + 1 - x³ - 6x² - 12x - 8 = -3x² - 9x - 7

Therefore, the simplified form of the expression is y = -3x² - 9x - 7.

2. 4 = (2 - 1)³ - (2 - 2)⁸

To simplify this expression, we substitute the given values:

4 = (1)³ - (0)⁸ = 1 - 0 = 1

Therefore, the equation is not satisfied, as 4 is not equal to 1.

3. y = (x - 1)³ • (x - 2) - (x - 2)² • (x - 1)

To simplify this expression, we can expand the cubes and squares using the binomial expansion formula:

(x - 1)³ = x³ - 3x² + 3x - 1 (x - 2)² = x² - 4x + 4

Substituting these expanded forms back into the original expression:

y = (x³ - 3x² + 3x - 1) • (x - 2) - (x² - 4x + 4) • (x - 1) = x⁴ - 4x³ + 4x² - 2x³ + 8x² - 8x + x² - 4x + 4 - x³ + 4x² - 4x - 3x² + 12x - 12 = x⁴ - 4x³ - 2x³ - x³ + 4x² + 8x² + x² - 3x² + 4x² - 4x + 12x - 4x + 4 - 12 = x⁴ - 7x³ + 14x² + 4x - 8

Therefore, the simplified form of the expression is y = x⁴ - 7x³ + 14x² + 4x - 8.