Question

Раскройте скобки 1)(3a-b)²-(3a+b)²2)(a+(b-c))²​

Answer 1

Ответ:

1) -12ab

2) a²​+2ab+b²​-2bc+c²​-2ac

Объяснение:

1) (3a-b)²-(3a+b)²=9a²-6ab+b²-(9a²+6ab+b²)=9a²-6ab+b²-9a²-6ab-b²=-12ab

2) (a+b-c)²​=(a+b-c)*(a+b-c)=a²​+ab-ac+ab+b²​-bc-ac-bc+c²​=a²​+2ab+b²​-2bc+c²​-2ac

Answer 2

1. (3a - b)² - (3a + b)²

Let's expand the expression step by step:

First, let's expand (3a - b)²: (3a - b)² = (3a - b) * (3a - b) = (3a - b)(3a - b) = 9a² - 3ab - 3ab + b² = 9a² - 6ab + b²

Next, let's expand (3a + b)²: (3a + b)² = (3a + b) * (3a + b) = (3a + b)(3a + b) = 9a² + 3ab + 3ab + b² = 9a² + 6ab + b²

Now, substitute the expanded expressions back into the original expression: (3a - b)² - (3a + b)² = (9a² - 6ab + b²) - (9a² + 6ab + b²)

To simplify, distribute the negative sign to both terms inside the parentheses: = 9a² - 6ab + b² - 9a² - 6ab - b²

Combine like terms: = (9a² - 9a²) + (-6ab - 6ab) + (b² - b²) = 0 - 12ab + 0 = -12ab

Therefore, (3a - b)² - (3a + b)² simplifies to -12ab.

2. (a + (b - c))²

Let's expand the expression:

(a + (b - c))² = (a + (b - c))(a + (b - c))

Using the distributive property, we can multiply each term:

= a(a + (b - c)) + (b - c)(a + (b - c))

Now let's multiply each term within the parentheses:

= a(a + b - c) + (b - c)(a + b - c)

Use the distributive property again:

= a² + ab - ac + (b(a + b - c) - c(a + b - c))

Expand further:

= a² + ab - ac + (ab + b² - bc - ac - bc + c²)

Now simplify:

= a² + ab - ac + ab + b² - bc - ac - bc + c²

Combine like terms:

= a² + 2ab - 2ac + b² - 2bc + c²

Therefore, (a + (b - c))² simplifies to a² + 2ab - 2ac + b² - 2bc + c².