Question

Выполните действия : а) (12y-5yx+2)-(2y-25yx) б) 2x³(x²-4) в) 2x³(4x+3)-8x⁴

Answer 1

А) (12у-5ух+2)-(2у-25ух)
(12у-5ху+2)-(2у-25ху)
12у-5ху+2-2у+25ху
10у+20ху+2
Ответ: 10у+20ху+2 ( в столбик )
б) 2х³(х²-4)
2х³х²-2х³×4
2х^5(в пятой)-8х³
Ответ:2х^5-8х³
в)2х³(4х+3)-8х⁴
8х⁴+6х³-8х⁴
6х³
Ответ: 6х³

Answer 2

a) (12y-5yx+2) - (2y-25yx)

To solve this expression, we need to combine like terms.

First, let's remove the parentheses by distributing the negative sign to each term inside the second parentheses:

(12y - 5yx + 2) - (2y - 25yx) = 12y - 5yx + 2 - 2y + 25yx

Now, let's combine like terms:

(12y - 2y) + (-5yx + 25yx) + 2 = 10y + 20yx + 2

So the simplified expression is 10y + 20yx + 2.

б) 2x³(x²-4)

To simplify this expression, we need to multiply the terms inside the parentheses by 2x³.

Using the distributive property, we multiply 2x³ by each term inside the parentheses:

2x³(x² - 4) = 2x³ * x² - 2x³ * 4

Simplifying further:

2x³ * x² = 2x^(3+2) = 2x^5

2x³ * 4 = 8x³

Putting it all together:

2x³(x² - 4) = 2x^5 - 8x³

So the simplified expression is 2x^5 - 8x³.

в) 2x³(4x+3) - 8x⁴

Similar to the previous expression, we need to distribute 2x³ to each term inside the parentheses:

2x³(4x + 3) - 8x⁴ = 2x³ * 4x + 2x³ * 3 - 8x⁴

Simplifying further:

2x³ * 4x = 8x^(3+1) = 8x⁴

2x³ * 3 = 6x^(3+1) = 6x⁴

Putting it all together:

2x³(4x + 3) - 8x⁴ = 8x⁴ + 6x⁴ - 8x⁴

Combining like terms:

8x⁴ + 6x⁴ - 8x⁴ = 6x⁴

So the simplified expression is 6x⁴.

I hope this helps! Let me know if you have any further questions.