Question

If Розкрийте дужки і спростіть 3(х2 + 2х - 5) - х(х +1) ​

Answer 1

3(x² + 2x - 5) - x(x + 1) = 3x² + 6x - 15 - x² - x = 2x² + 5x - 15

Answer 2

$3(x {}^{2} + 2x - 5) - x(x + 1) = 3x {}^{2} + 6x - 15 - x {}^{2} - x = 2x {}^{2} + 5x - 15$

использовали распределительное свойство: а(b+c)=ab+ac.

Answer 3

I will answer in detail. To simplify the expression 3(х2 + 2х - 5) - х(х + 1), we need to follow these steps:

- First, we need to expand the brackets by multiplying each term inside the brackets by the term outside the brackets. For example, 3(х2 + 2х - 5) means 3 times х2, plus 3 times 2х, minus 3 times 5. We use the distributive property of multiplication over addition and subtraction to do this. - Second, we need to simplify the expression by combining the like terms. Like terms are terms that have the same variable raised to the same power. For example, 6х2 and 2х2 are like terms, but 6х2 and 2х are not. We can add or subtract the coefficients of the like terms to simplify the expression. - Third, we need to write the final answer in the standard form, which means arranging the terms in descending order of their degree (the highest power of the variable). For example, the standard form of 2х + 6х2 - 5 is 6х2 + 2х - 5.

Using these steps, we can simplify the expression 3(х2 + 2х - 5) - х(х + 1) as follows:

3(х2 + 2х - 5) - х(х + 1) = 3х2 + 6х - 15 - х2 - х (expand the brackets) = 3х2 - х2 + 6х - х - 15 (rearrange the terms) = 2х2 + 5х - 15 (combine the like terms) = 2х2 + 5х - 15 (write the final answer in the standard form)

Therefore, the simplified expression is 2х2 + 5х - 15.

You can also use online calculators to check your answer or to simplify expressions automatically. For example, you can use the online calculator [here](https://allcalc.ru/node/1826) to expand the brackets or the online calculator [here](https://allcalc.ru/node/1825) to simplify the expression. You can also find some examples and explanations of how to simplify expressions [here](https://school.home-task.com/virazi-ta-yix-sproshhennya/) or [here](https://naurok.com.ua/prezentaciya-mnozhennya-odnochlena-na-mnogochlen-7-klas-263385.html).