Question

Почему (2y - x) в квадрате это тоже самое, что и (x - 2y) в квадрате Если это не так, объясните почему

Answer 1

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Answer 2

-1*-1=1; (-1)²=1;

(2y-x)²=(1*(2y-x))²=(-1*-1*(2y-x))²=(-1*(-1*2y-(-1)*x))²=(-1*(-2y+x))²=(-1)²(-2y+x)²=1*(x-2y)²=(x-2y)²;

Answer 3

(2y - x)^2 and (x - 2y)^2 are not the same, and expanding each expression will show why:

Expanding (2y - x)^2: (2y - x)^2 = (2y - x)(2y - x) = 4y^2 - 2xy - 2xy + x^2 = 4y^2 - 4xy + x^2

Expanding (x - 2y)^2: (x - 2y)^2 = (x - 2y)(x - 2y) = x^2 - 2xy - 2xy + 4y^2 = x^2 - 4xy + 4y^2

As you can see, the two expanded expressions are different:

• (2y - x)^2 expands to 4y^2 - 4xy + x^2
• (x - 2y)^2 expands to x^2 - 4xy + 4y^2

The only similarity between the two is that they both contain the terms 4y^2 and -4xy, but they have different coefficients for these terms. This is because when we square any binomial (a - b)^2, we get a^2 - 2ab + b^2, not a^2 - 2ab - 2ab + b^2.

In conclusion, (2y - x)^2 and (x - 2y)^2 are not the same. They differ in the coefficient of the xy term, which means they represent different algebraic expressions.