Question

Перетворіть вираз на многочлен 1. (3а+7b)(7b - 3а): 2. (8b² - 3x⁴p)(8b² + 3x⁴p); 3. (9x + 4y)2; 4. (2m² - 2,25n)². ​

Answer 1

Ответ:...

Объяснение:

1)(3a + 7b)(7b - 3a) = (3a)^2 - (7b)^2 = 9a^2 - 49b^2-многочлен

2)(8b² - 3x⁴p)(8b² + 3x⁴p) = (8b²)² - (3x⁴p)²= 64b⁴ - 9x⁸p²-многочлен

4)(a + b)² = a² + 2ab + b²

Де a = 2m² і b = -2,25n. Тоді:

(2m² - 2,25n)² = (2m²)² + 2(2m²)(-2,25n) + (-2,25n)²

= 4m^4 - 9m²n + 5,0625n²

Отже, (2m² - 2,25n)² можна спростити до многочлена 4m^4 - 9m²n + 5,0625n²

Answer 2

1. (3a + 7b)(7b - 3a): Expanding the expression using the distributive property: (3a + 7b)(7b - 3a) = 3a * 7b - 3a * 3a + 7b * 7b - 3a * 7b Simplifying further: 21ab - 9a^2 + 49b^2 - 21ab Combining like terms: -9a^2 + 49b^2

2. (8b² - 3x⁴p)(8b² + 3x⁴p): Expanding the expression using the distributive property: (8b² - 3x⁴p)(8b² + 3x⁴p) = 8b² * 8b² + 8b² * 3x⁴p - 3x⁴p * 8b² - 3x⁴p * 3x⁴p Simplifying further: 64b^4 + 24b²x⁴p - 24b²x⁴p - 9x⁸p² Combining like terms: 64b^4 - 9x⁸p²

3. (9x + 4y)²: Expanding the expression using the square of a binomial formula: (9x + 4y)² = (9x)² + 2 * (9x) * (4y) + (4y)² Simplifying further: 81x² + 72xy + 16y²

4. (2m² - 2.25n)²: Expanding the expression using the square of a binomial formula: (2m² - 2.25n)² = (2m²)² - 2 * (2m²) * (2.25n) + (2.25n)² Simplifying further: 4m^4 - 9n^2 + 10.0625n²