Question

ПОЖАЛУЙСТА РЕШИТЕ 1) (15x+a)³2)a³-64x=РАЗЛАЖЕНИЕ НА МНОЖИТЕЛИ МЕДОДОМ ГРУППЕРОВКИЗДЕЛАЙТЕ ПОЖАЛУЙСТА СРОЧНО ПОЖААААААААЛУЙСТА ДАЮ 10 БАЛЛОВ

Answer 1

Ответ:

Пошаговое объяснение:

1) (15x+a)³=(15x+a)(225x^2-15ax+a^2);

2)a³-64x³=(a-4x)(a^2+4ax+16x^2).

Answer 2

1) To solve the expression (15x + a)^3, we can use the binomial expansion formula. The formula states that for any binomial expression (a + b)^n, the expansion can be found using the binomial coefficients and the powers of a and b. In this case, we have (15x + a)^3, so we can expand it as follows:

(15x + a)^3 = C(3,0)*(15x)^3*a^0 + C(3,1)*(15x)^2*a^1 + C(3,2)*(15x)^1*a^2 + C(3,3)*(15x)^0*a^3

where C(n, k) represents the binomial coefficient, given by C(n, k) = n! / (k! * (n-k)!).

Simplifying the above expression, we get:

(15x + a)^3 = (15x)^3 + 3*(15x)^2*a + 3*(15x)*a^2 + a^3

So, the expression (15x + a)^3 can be expanded as (15x)^3 + 3*(15x)^2*a + 3*(15x)*a^2 + a^3.

2) To factorize the expression a^3 - 64x, we can use the difference of cubes formula. The formula states that for any expression of the form a^3 - b^3, it can be factorized as (a - b)*(a^2 + ab + b^2).

In this case, we have a^3 - 64x, which can be written as (a)^3 - (4x)^3. Therefore, we can factorize it as:

a^3 - 64x = (a - 4x)*(a^2 + a*4x + (4x)^2)

Simplifying further, we get:

a^3 - 64x = (a - 4x)*(a^2 + 4ax + 16x^2)

So, the expression a^3 - 64x can be factorized as (a - 4x)*(a^2 + 4ax + 16x^2).

Please note that the above factorizations are derived using mathematical formulas and techniques.