Question

(a+4)²-(b+2)² (x-5)²-(y+8)² (m-10)²-(n-12)² 121-(b-13)² 5a²+10ab+5b² Если можно все

Answer 1

(a+4)²-(b+2)²= разложим как разницу квадратов
(а+4-в-2)(а+4+в+2)= приведём подобные в каждой скобочке
(а-в+2)(а+в+6).

(x-5)²-(y+8)²= разложим как разницу квадратов
(х-5-у-8)(х-5+у+8)= приведём подобные
(х-у-13)(х+у+3).

(m-10)²-(n-12)²= разложим как разницу квадратов
(м-10-н+12)(м-10+н-12)=приведём подобные
(м-н+2)(м+н-22).

121-(b-13)²=представим 121 как квадрат одиннадцати
11²-(в-13)²= разложим как разницу квадратов
(11-в+13)(11+в-13)=приведём подобные
(24-в)(в-2).

5a²+10ab+5b²=вынесем за скобки пятёрку
5(а²+2ав+в²)=свернём квадрат суммы
5(а+в)².

Answer 2

Sure, let's simplify the given expressions:

1. (a+4)² - (b+2)²: Using the formula for the difference of squares: (a² - b²) = (a + b)(a - b), we can simplify this expression as follows: (a+4)² - (b+2)² = [(a + 4) + (b + 2)][(a + 4) - (b + 2)] = (a + b + 6)(a - b + 2)

2. (x-5)² - (y+8)²: Using the formula for the difference of squares: (a² - b²) = (a + b)(a - b), we can simplify this expression as follows: (x-5)² - (y+8)² = [(x - 5) + (y + 8)][(x - 5) - (y + 8)] = (x + y + 3)(x - y - 13)

3. (m-10)² - (n-12)²: Using the formula for the difference of squares: (a² - b²) = (a + b)(a - b), we can simplify this expression as follows: (m-10)² - (n-12)² = [(m - 10) + (n - 12)][(m - 10) - (n - 12)] = (m + n - 22)(m - n - 2)

4. 121 - (b-13)²: Using the formula for the difference of squares: (a² - b²) = (a + b)(a - b), we can simplify this expression as follows: 121 - (b-13)² = 121 - [(b - 13) + (b - 13)][(b - 13) - (b - 13)] = 121 - (2b - 26)(-26) = 121 - 4(b - 13) = 121 - 4b + 52 = 173 - 4b

5. 5a² + 10ab + 5b²: This is a trinomial and doesn't have a straightforward factorization. However, it can be simplified to the square of a binomial as follows: 5a² + 10ab + 5b² = 5(a² + 2ab + b²) = 5(a + b)²

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.