Question

СРОЧНО!!! (a-b+c)²-(a-b-c)²=​

Answer 1

используем формулу х²-у²=(х-у)(х+у)

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

((a-b+c-a+b+c))*​((a-b+c+a-b-c))=​2с*(2а-2b)=4ас-4bс

Answer 2

To simplify the expression "(a-b+c)² - (a-b-c)²," we can use the identity for the difference of squares, which states that:

(a² - b²) = (a + b)(a - b)

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

Step 1: Expand the first square.

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

Step 2: Expand the second square.

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

Step 3: Subtract the expanded second square from the expanded first square.

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

Notice that all the terms except "2ab," "2ac," and "2bc" cancel out when subtracting the two expressions.

So, the final result is:

(a - b + c)² - (a - b - c)² = 2ab - 2ac + 2bc

That's the simplified form of the given expression.