Question

Розклпдіть на множники ab³-9a³b​

Answer 1

Ответ:

$ab {}^{3} - 9a {}^{3} b = ab(b {}^{2} - 9a {}^{2} ) = ab(b - 3a)(b + 3a)$

Answer 2

Factoring the Expression ab³ - 9a³b

To factor the expression ab³ - 9a³b, we can first look for common factors in the terms. Then, we can use the difference of cubes formula to factorize the expression.

1. Identifying Common Factors: - The expression ab³ - 9a³b contains two terms: ab³ and 9a³b. - Both terms have a common factor of ab.

2. Using the Difference of Cubes Formula: - The expression ab³ - 9a³b can be rewritten as (ab)³ - (3a)³(b)³. - According to the difference of cubes formula, a³ - b³ = (a - b)(a² + ab + b²).

3. Factoring the Expression: - Applying the difference of cubes formula, we can factorize ab³ - 9a³b as follows: - ab³ - 9a³b = (ab - 3a)(a²b² + 3ab + 9b²).

Therefore, the factored form of the expression ab³ - 9a³b is (ab - 3a)(a²b² + 3ab + 9b²).