Question

Представьте выражения в виде многочлена: 1) (3ab-2)^3 2)(4x^2y-5)^3 3) (-2a^2+b^3)^3 4) (-3a-2b^2)^3 5)(a^n+2)^3 6) (3-x^n)^3 7) (x^n-1 -3x)^3 8)(a^n+1 +4a)^3 Пожалуйста помогите,заранее огромное вам спасибо.

Answer 1

1)(3ab)^3-3(3ab)^2*2+3*3ab*2^2-2^3=27a^3b^3-54a^2b^2+36ab-8

Answer 2

Expressions as Polynomials:

Let's represent the given expressions as polynomials:

1) (1) 2) (3ab-2)^3 3) (4x^2y-5)^3 4) (-2a^2+b^3)^3 5) (-3a-2b^2)^3 6) (a^n+2)^3 7) (3-x^n)^3 8) (x^n-1-3x)^3 9) (a^n+1+4a)^3

Now, let's expand each expression and simplify them:

1) (1): The expression is already in its simplest form.

2) (3ab-2)^3: Expanding this expression using the binomial theorem, we get: (3ab-2)^3 = (3ab)^3 - 3(3ab)^2(2) + 3(3ab)(2^2) - 2^3 Simplifying further, we have: (3ab-2)^3 = 27a^3b^3 - 54a^2b^2 + 36ab - 8 3) (4x^2y-5)^3: Expanding this expression using the binomial theorem, we get: (4x^2y-5)^3 = (4x^2y)^3 - 3(4x^2y)^2(5) + 3(4x^2y)(5^2) - 5^3 Simplifying further, we have: (4x^2y-5)^3 = 64x^6y^3 - 240x^4y^2 + 300x^2y - 125 4) (-2a^2+b^3)^3: Expanding this expression using the binomial theorem, we get: (-2a^2+b^3)^3 = (-2a^2)^3 - 3(-2a^2)^2(b^3) + 3(-2a^2)(b^3)^2 - (b^3)^3 Simplifying further, we have: (-2a^2+b^3)^3 = -8a^6 + 12a^4b^3 - 6a^2b^6 + b^9 5) (-3a-2b^2)^3: Expanding this expression using the binomial theorem, we get: (-3a-2b^2)^3 = (-3a)^3 - 3(-3a)^2(2b^2) + 3(-3a)(2b^2)^2 - (2b^2)^3 Simplifying further, we have: (-3a-2b^2)^3 = -27a^3 + 54a^2b^2 - 36ab^4 + 8b^6 6) (a^n+2)^3: Expanding this expression using the binomial theorem, we get: (a^n+2)^3 = (a^n)^3 + 3(a^n)^2(2) + 3(a^n)(2^2) + 2^3 Simplifying further, we have: (a^n+2)^3 = a^3n + 6a^2n + 12an^2 + 8 7) (3-x^n)^3: Expanding this expression using the binomial theorem, we get: (3-x^n)^3 = (3)^3 - 3(3)^2(x^n) + 3(3)(x^n)^2 - (x^n)^3 Simplifying further, we have: (3-x^n)^3 = 27 - 54x^n + 27x^2n - x^3n 8) (x^n-1-3x)^3: Expanding this expression using the binomial theorem, we get: (x^n-1-3x)^3 = (x^n-1)^3 - 3(x^n-1)^2(3x) + 3(x^n-1)(3x)^2 - (3x)^3 Simplifying further, we have: (x^n-1-3x)^3 = x^3n - 3x^2n + 3xn - 1 - 9x^2n + 9xn - 27x^3 + 27x^2 - 9x 9) (a^n+1+4a)^3: Expanding this expression using the binomial theorem, we get: (a^n+1+4a)^3 = (a^n+1)^3 + 3(a^n+1)^2(4a) + 3(a^n+1)(4a)^2 + (4a)^3 Simplifying further, we have: (a^n+1+4a)^3 = a^3n + 3a^2n + 3an^2 + 1 + 12a^2n + 24an^2 + 48a^3 + 48a^2 + 12a I hope this helps! Let me know if you have any further questions.

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