Question

(a+b+c)²-(a-b-c)² разложить на множители

Answer 1

4а× (а+б+с)


........

Answer 2

(a+b+c-a+b+c)*(a+b+c+a-b-c)=(2a+2b+2c)*2a=4a*(a+b+c)

Answer 3

To factor the expression (a+b+c)² - (a-b-c)², we can use the difference of squares formula, which states that:

(a² - b²) = (a + b)(a - b)

Let's apply this formula to the given expression step by step:

Step 1: Identify (a+b+c)² as the first term and (a-b-c)² as the second term.

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

Step 2: Apply the difference of squares formula to both terms.

(a + b + c)(a + b + c) - (a - b - c)(a - b - c) = [(a + b)² + 2(a + b)c + c²] - [(a - b)² - 2(a - b)c + c²]

Step 3: Expand both squares.

= [(a² + 2ab + b²) + 2(a + b)c + c²] - [(a² - 2ab + b²) - 2(a - b)c + c²]

Step 4: Remove the square brackets.

= a² + 2ab + b² + 2(a + b)c + c² - a² + 2ab - b² - 2(a - b)c + c²

Step 5: Simplify the expression.

= 4ab + 2c(a + b - a + b) + c² + c² = 4ab + 4bc + 2c²

Now, the factored expression is:

(a+b+c)² - (a-b-c)² = 4ab + 4bc + 2c²