Question

M² + n² = (m+n)² - 2mn

Answer 1

Ответ:

(m+n)² - 2mn = m² + 2mn + n² - 2mn = m² + n²

Объяснение:

Розкриваємо праву частину за допомогою формули скороченого множення.

Таким чином, рівняння має безліч розв'язків, оскільки воно тотожне.

Answer 2

The equation $m^2 + n^2 = (m + n)^2 - 2mn$ is a mathematical identity, also known as the "binomial square formula" or the "algebraic identity." It demonstrates the relationship between the sum of two squares (the left side) and the square of their sum minus twice their product (the right side).

To prove this identity, you can expand the expressions on both sides:

Left side: $m^2 + n^2$

Right side: $(m + n)^2 - 2mn = (m + n)(m + n) - 2mn$ $= (m^2 + 2mn + n^2) - 2mn$

Now, if you simplify the right side by combining like terms, you'll see that it equals the left side:

$m^2 + 2mn + n^2 - 2mn = m^2 + n^2$

So, $m^2 + n^2 = (m + n)^2 - 2mn$ is indeed a valid identity, and you can use it in various algebraic manipulations and proofs.