Question

48x²y²+9+64x⁴y⁴=(___)²=(___)(___) Помогите пожалуйста

Answer 1

Ответ:

(8x^2y^2+3)^2

Объяснение:

Answer 2

Factoring the Expression 48x²y² + 9 + 64x⁴y⁴

To factor the given expression 48x²y² + 9 + 64x⁴y⁴, we can recognize it as a sum of cubes. The sum of cubes formula is given by:

a³ + b³ = (a + b)(a² - ab + b²)

In this case, we can express 48x²y² as (4xy)² and 64x⁴y⁴ as (8x²y²)². The 9 can be expressed as 3².

So, the given expression can be factored as:

48x²y² + 9 + 64x⁴y⁴ = (4xy)² + 3² + (8x²y²)²

Using the sum of cubes formula, we can factor it further:

= (4xy + 3)(16x⁴y⁴ - 12x²y² + 9)

Therefore, the factored form of the expression 48x²y² + 9 + 64x⁴y⁴ is (4xy + 3)(16x⁴y⁴ - 12x²y² + 9).