Question

Внести НОД за скобки 1)90а+72b+18c. 2)63a+99b+135c. Помогите пожалуйста

Answer 1

1) 9 * (10а + 8b + 2с)
2) 9 * (7а + 11b + 15с)

Answer 2

6 (2х+3у+8)
14 (3х+2у+7)
18 (5а+4b+с)
9 (7a+11b+5c)

Answer 3

Finding the Greatest Common Divisor (GCD)

To find the greatest common divisor (GCD) for the given expressions, we can use the method of prime factorization. First, we'll factorize each expression and then find the common factors.

1) 90a + 72b + 18c 2) 63a + 99b + 135c

Factorization of the Expressions

1) 90a + 72b + 18c - Factorizing each term individually: - 90a = 2 * 3^2 * 5 * a - 72b = 2^3 * 3^2 * b - 18c = 2 * 3^2 * c - So, the expression can be written as: 2 * 3^2 * (5a + 4b + c)

2) 63a + 99b + 135c - Factorizing each term individually: - 63a = 3^2 * 7 * a - 99b = 3^2 * 11 * b - 135c = 3^3 * 5 * c - So, the expression can be written as: 3^2 * (7a + 11b + 15c)

Finding the GCD

Now, we'll find the common factors in the two expressions to determine the GCD.

The common factors are: - 2 - 3^2

So, the greatest common divisor (GCD) for the given expressions is 2 * 3^2, which is 18.

Therefore, the GCD for the given expressions 90a + 72b + 18c and 63a + 99b + 135c is 18.