Question

Разложи на множители 1)7m-n +49m² -n² 2) 5m-n +25m² -n² 3) 4) x² - 2xy + y²-9 4x² - 4xy + y² - 16​

Answer 1

Разложим выражение на 2 квадрата биномов: 7m - n + 49m² - n² = (7m + 7n + n)(7m - 7n - n) = (7m + 7n + n)(7m - 8n)

Разложим выражение на 2 квадрата биномов: 5m - n + 25m² - n² = (5m + 5n + n)(5m - 6n) = (5m + 6n)(5m - n)

Разложим выражение на квадрат бинома: x² - 2xy + y² - 9 = (x - y)² - 9 = (x - y + 3)(x - y - 3)

Разложим выражение на квадрат бинома: 4x² - 4xy + y² - 16 = (2x - y)² - 16 = (2x - y + 4)(2x - y - 4)

Answer 2

Ответ:

решение смотри на фотографии

Answer 3

1. To factorize the expression 7m-n + 49m² - n², we can group the terms as follows:

(7m - n) + (49m² - n²)

Now, we can observe that (7m - n) is similar to the form of a² - b², which can be factored as (a + b)(a - b). Similarly, (49m² - n²) is in the form of (a² - b²), where a = 7m and b = n. So, we have:

(7m - n) + (49m² - n²) = (7m - n) + (7m + n)(7m - n)

Therefore, the expression can be factored as (7m - n) + (7m + n)(7m - n).

2. To factorize the expression 5m-n + 25m² - n², we can follow a similar approach:

(5m - n) + (25m² - n²) = (5m - n) + (5m + n)(5m - n)

Therefore, the expression can be factored as (5m - n) + (5m + n)(5m - n).

3. To factorize the expression x² - 2xy + y² - 9, we can rewrite it as:

(x² - 2xy + y²) - 9

Now, the expression x² - 2xy + y² is a perfect square trinomial and can be factored as (x - y)². Therefore, we have:

(x - y)² - 9

This is a difference of squares, which can be factored as (x - y - 3)(x - y + 3). Hence, the expression can be factored as (x - y - 3)(x - y + 3).

4. To factorize the expression 4x² - 4xy + y² - 16, we can follow a similar approach:

(4x² - 4xy + y²) - 16 = (2x - y)² - 16 = ((2x - y) - 4)((2x - y) + 4)

Therefore, the expression can be factored as ((2x - y) - 4)((2x - y) + 4).