Question

Решите пожалуйста 1)(c²-6)² 2)(15+k²)² 3)(m²-3n)² 4)(m^4-n^3)² 5)(5a^4-2a^7)²

Answer 1

1)(c²-6)²=c^4-12c²+36
2)(15+k²)²=225+30k²+k^4
3)(m²-3n)²=m^4-6m²n+9n²
4)(m^4-n^3)²=m^8-2m^4*n³+n^6
5)(5a^4-2a^7)²=25a^8-20a^11+4a^14

Answer 2

1. (c² - 6)²: To solve this expression, we can apply the formula for squaring a binomial, which states that (a - b)² = a² - 2ab + b². In this case, our binomial is (c² - 6).

Applying the formula, we have: (c² - 6)² = (c²)² - 2(c²)(6) + (6)² = c⁴ - 12c² + 36

Therefore, the solution is c⁴ - 12c² + 36.

2. (15 + k²)²: Following the same approach as before, we can expand this expression using the formula for squaring a binomial.

(15 + k²)² = (15)² + 2(15)(k²) + (k²)² = 225 + 30k² + k⁴

The solution is 225 + 30k² + k⁴.

3. (m² - 3n)²: Expanding this expression using the formula for squaring a binomial:

(m² - 3n)² = (m²)² - 2(m²)(3n) + (3n)² = m⁴ - 6m²n + 9n²

The solution is m⁴ - 6m²n + 9n².

4. (m⁴ - n³)²: Using the same approach as before:

(m⁴ - n³)² = (m⁴)² - 2(m⁴)(n³) + (n³)² = m⁸ - 2m⁴n³ + n⁶

The solution is m⁸ - 2m⁴n³ + n⁶.

5. (5a⁴ - 2a⁷)²: Applying the formula for squaring a binomial:

(5a⁴ - 2a⁷)² = (5a⁴)² - 2(5a⁴)(2a⁷) + (2a⁷)² = 25a⁸ - 20a¹¹ + 4a¹⁴

The solution is 25a⁸ - 20a¹¹ + 4a¹⁴.