Question

(7х-а)²=?(5с-1)(5с+1)=?(3х-5у)(3х+5у)=?(5у-3х)²=?​

Answer 1

$\displaystyle (7x-a)^2=(7x)^2-2*7x*a+a^2=49x^2-14xa+a^2\\\\(5c-1)(5c+1)=(5c)^2-1^2=25c^2-1\\\\(3x-5y)(3x+5y)=(3x)^2-(5y)^2=9x^2-25y^2\\\\(5y-3x)^2=(5y)^2-2*5y*3x+(3x)^2=25y^2-30yx+9x^2$

Воспользовались формулами сокращенного умножения

$\displaystyle a^2-b^2=(a-b)(a+b)\\\\(a-b)^2=a^2-2ab+b^2$

Answer 2

To simplify the given expressions, let's expand each of them:

1. (7x - a)²: Using the formula (a - b)² = a² - 2ab + b², we can expand (7x - a)² as follows: (7x - a)² = (7x)² - 2(7x)(a) + a² = 49x² - 14ax + a²

2. (5c - 1)(5c + 1): Using the formula (a - b)(a + b) = a² - b², we can expand (5c - 1)(5c + 1) as follows: (5c - 1)(5c + 1) = (5c)² - (1)² = 25c² - 1

3. (3x - 5y)(3x + 5y): Using the formula (a - b)(a + b) = a² - b², we can expand (3x - 5y)(3x + 5y) as follows: (3x - 5y)(3x + 5y) = (3x)² - (5y)² = 9x² - 25y²

4. (5y - 3x)²: Using the formula (a - b)² = a² - 2ab + b², we can expand (5y - 3x)² as follows: (5y - 3x)² = (5y)² - 2(5y)(3x) + (3x)² = 25y² - 30xy + 9x²

Therefore, the expanded forms of the given expressions are:

1. (7x - a)² = 49x² - 14ax + a²
2. (5c - 1)(5c + 1) = 25c² - 1
3. (3x - 5y)(3x + 5y) = 9x² - 25y²
4. (5y - 3x)² = 25y² - 30xy + 9x²