Question

(x+√y)(x-√y)+(x-√y)^2

Answer 1

Ответ:

(x+√y)(x-√y)+(x-√y)^2=x²-(√y)²+x²-x√y+(√y)²=x²-y+x²-x√y+y=x²+x²-x√y=2x²-x√y=x(2x-√y)

Объяснение:

(a-b)²=a²-2ab+b²

a²-b²=(a-b)(a+b)

Answer 2

Let's simplify the expression step by step:

Step 1: Expand the first term (x + √y)(x - √y): (x + √y)(x - √y) = x(x) + x(-√y) + √y(x) + √y(-√y) = x^2 - x√y + x√y - y = x^2 - y

Step 2: Expand the second term (x - √y)^2: (x - √y)^2 = (x - √y)(x - √y) = x(x) - x(√y) - √y(x) + √y(√y) = x^2 - x√y - x√y + y = x^2 - 2x√y + y

Step 3: Add the results from Step 1 and Step 2: (x + √y)(x - √y) + (x - √y)^2 = (x^2 - y) + (x^2 - 2x√y + y) = x^2 - y + x^2 - 2x√y + y = 2x^2 - 2x√y

So, the simplified expression is 2x^2 - 2x√y.