Question

Представьте в виде многочлена. 1)(2m-3n)^3. 2)(4a+1/3b)^3. 3)(2x-1/2y)^3

Answer 1

1)8m^3-3×4m^2×(-3n)+3×2m× 9n^2-27n^3=8m^3+36m^2n+54mn^2-27n^3

Answer 2

ВСЁ ОЧЕНЬ просто только подумай 

Answer 3

1) (2m-3n)^3

To expand the binomial (2m-3n)^3, we can use the binomial theorem or the method of multiplying out the terms. Using the binomial theorem, the expansion can be calculated as follows:

(2m-3n)^3 = C(3,0)(2m)^3(-3n)^0 + C(3,1)(2m)^2(-3n)^1 + C(3,2)(2m)^1(-3n)^2 + C(3,3)(2m)^0(-3n)^3

Here, C(n, r) denotes the binomial coefficient "n choose r," which is calculated as n! / (r! * (n-r)!), where ! denotes factorial.

Calculating the binomial coefficients and simplifying the terms, we get:

(2m-3n)^3 = 8m^3 - 12m^2n + 18mn^2 - 27n^3

So, the expanded form of (2m-3n)^3 is 8m^3 - 12m^2n + 18mn^2 - 27n^3.

2) (4a+1/3b)^3

To expand the binomial (4a+1/3b)^3, we can use the same method:

(4a+1/3b)^3 = C(3,0)(4a)^3(1/3b)^0 + C(3,1)(4a)^2(1/3b)^1 + C(3,2)(4a)^1(1/3b)^2 + C(3,3)(4a)^0(1/3b)^3

Calculating the binomial coefficients and simplifying the terms, we get:

(4a+1/3b)^3 = 64a^3 + 32a^2/3b + 16a/9b^2 + 1/27b^3

So, the expanded form of (4a+1/3b)^3 is 64a^3 + 32a^2/3b + 16a/9b^2 + 1/27b^3.

3) (2x-1/2y)^3

Similarly, for (2x-1/2y)^3:

(2x-1/2y)^3 = C(3,0)(2x)^3(-1/2y)^0 + C(3,1)(2x)^2(-1/2y)^1 + C(3,2)(2x)^1(-1/2y)^2 + C(3,3)(2x)^0(-1/2y)^3

After calculating the binomial coefficients and simplifying the terms, we get:

(2x-1/2y)^3 = 8x^3 - 6x^2y + 3xy^2 - 1/8y^3

So, the expanded form of (2x-1/2y)^3 is 8x^3 - 6x^2y + 3xy^2 - 1/8y^3.