Question

АЛГЕБРА!!! СРОЧНО!!! многочлены.умножение. 1) (x-1)(x-1)(2x+1) 2)(a-x)(a^2+x^2)(a+x) 3) (2x-1/2y) (4x^2+xy+0,25y^2) 4)(a+2b)((a-2b)^2+2ab)

Answer 1

Ответ:Фото

Объяснение:

Answer 2

1. (x-1)(x-1)(2x+1):

To multiply these polynomials, we can use the distributive property and simplify step by step.

First, let's multiply (x-1) with (x-1): (x-1)(x-1) = x(x) + x(-1) + (-1)(x) + (-1)(-1) = x^2 - x - x + 1 = x^2 - 2x + 1

Now, let's multiply the result by (2x+1): (x^2 - 2x + 1)(2x+1) = 2x(x^2 - 2x + 1) + 1(x^2 - 2x + 1) = 2x^3 - 4x^2 + 2x + x^2 - 2x + 1 = 2x^3 - 3x^2

So, the product is 2x^3 - 3x^2.

2. (a-x)(a^2+x^2)(a+x):

Similarly, we'll use the distributive property to multiply these polynomials.

First, let's multiply (a-x) with (a^2+x^2): (a-x)(a^2+x^2) = a(a^2+x^2) - x(a^2+x^2) = a^3 + ax^2 - ax - x^3

Now, let's multiply the result by (a+x): (a^3 + ax^2 - ax - x^3)(a+x) = a(a^3 + ax^2 - ax - x^3) + x(a^3 + ax^2 - ax - x^3) = a^4 + a^2x^2 - a^2x - ax^3 + a^3x + ax^3 - ax^2 - x^4 = a^4 + a^3x + a^2x^2 - a^2x - ax^2 - x^4

So, the product is a^4 + a^3x + a^2x^2 - a^2x - ax^2 - x^4.

3. (2x-1/2y) (4x^2+xy+0.25y^2):

Using the distributive property again, we'll multiply these polynomials.

(2x-1/2y) (4x^2+xy+0.25y^2) = 2x(4x^2+xy+0.25y^2) - (1/2y)(4x^2+xy+0.25y^2) = 8x^3 + 2x^2y + 0.5xy^2 - 2x^2 - 0.5xy - 0.125y^2

So, the product is 8x^3 + 2x^2y + 0.5xy^2 - 2x^2 - 0.5xy - 0.125y^2.

4. (a+2b)((a-2b)^2+2ab):

Let's simplify this expression step by step.

First, let's expand (a-2b)^2: (a-2b)^2 = (a-2b)(a-2b) = a(a) - 2b(a) - 2b(a) + 2b(2b) = a^2 - 2ab - 2ab + 4b^2 = a^2 - 4ab + 4b^2

Now, let's multiply (a+2b) by the result: (a+2b)(a^2 - 4ab + 4b^2) = a(a^2 - 4ab + 4b^2) + 2b(a^2 - 4ab + 4b^2) = a^3 - 4a^2b + 4ab^2 + 2ab^2 - 8b^3 + 8b^3 = a^3 - 4a^2b + 6ab^2

So, the product is a^3 - 4a^2b + 6ab^2.