Question

1) 36а⁴-25а²b²2) (x-7)²-81 разложить на множители

Answer 1

1)36a^4 -25a^2b^2 =(6a^2)^2- (5ab)^2=(6a^2-5ab)(6a^2+5ab);
2)(x-7)^2-81 =(x-7)^2-9^2=(x-7 -9)(x-7+9)=(x-16)(x+2)

Answer 2

Это разница квадратов

Answer 3

To factorize the given expressions, let's take them one by one:

1. Factorization of 36a⁴ - 25a²b²:

To factorize this expression, notice that it follows the pattern of the difference of squares. The expression can be written as (6a²)² - (5ab)². Now, we can use the difference of squares formula, which states that a² - b² = (a + b)(a - b).

So, applying this formula, we get:

36a⁴ - 25a²b² = (6a² + 5ab)(6a² - 5ab).

2. Factorization of (x - 7)² - 81:

This expression is in the form of a difference of squares, as well. It can be written as (x - 7)² - 9².

Now, we use the difference of squares formula again:

(x - 7)² - 81 = [(x - 7) + 9][(x - 7) - 9] = (x + 2)(x - 16).

So, the factorization of the given expression is (x + 2)(x - 16).