Question

Даю 15 баллов!Решите ПОДРОБНО m³-6m²n+12mn²-8n³.

Answer 1

Ответ:

m³-3-m²*2n+3m*4n²-2³n³

m³-3m²*2n+3*2²n²-(2n)³

m³-3*x²*2n+3m*(2n)²-(2n)³

(m-2n)³

Объяснение:

Answer 2

To solve the expression m³ - 6m²n + 12mn² - 8n³, we can factor it by grouping. Here's how:

Step 1: Grouping

First, let's group the terms in pairs:

(m³ - 6m²n) + (12mn² - 8n³)

Step 2: Factor out common factors

Now, let's factor out the common factors from each pair:

m²(m - 6n) + 4n²(3m - 2n)

Step 3: Factor out common factors again

Next, let's factor out the common factors from the entire expression:

m²(m - 6n) + 4n²(3m - 2n)

Step 4: Simplify

Finally, we have factored the expression as much as possible. The simplified form is:

m²(m - 6n) + 4n²(3m - 2n)

And that's the detailed solution to the expression m³ - 6m²n + 12mn² - 8n³.