Question

X²-4xy+4y²-4x+8y+7, если x-2y=4

Answer 1

$x^{2} -4xy + 4y^{2} - 4x + 8y + 7 = (x - 2y)^{2} - 4(x - 2y)+ 7 =\\= 4^{2} - 4 \cdot 4 + 7 = 7$

Answer 2

$x - 2y = 4 \\ x = 2y + 4 \\ x {}^{2} - 4xy + 4y {}^{2} - 4x + 8y + 7 = \\ (2y + 4) {}^{2} - 4y(2y + 4) + 4y {}^{2} - 4(2y + 4) + 8y + 7 = \\ 4y {}^{2} + 16y + 16 - 8y {}^{2} - 16y + 4y {}^{2} - 8y - 16 + 8y + 7 = \\ 16 - 16 + 7 = 7$

Answer 3

To find the value of the expression $x^2 - 4xy + 4y^2 - 4x + 8y + 7$ when $x - 2y = 4$, we first need to express one variable in terms of the other using the given equation $x - 2y = 4$. Once we have the value of one variable, we can substitute it into the expression and calculate the result.

Step 1: Express $x$ in terms of $y$ using the equation $x - 2y = 4$: $x = 4 + 2y$

Step 2: Substitute the value of $x$ from Step 1 into the expression: $x^2 - 4xy + 4y^2 - 4x + 8y + 7 = (4 + 2y)^2 - 4(4 + 2y)y + 4y^2 - 4(4 + 2y) + 8y + 7$

Step 3: Simplify the expression: $x^2 - 4xy + 4y^2 - 4x + 8y + 7 = (16 + 16y + 4y^2) - (16y + 8y^2) + 4y^2 - (16 + 8y) + 8y + 7$

Step 4: Combine like terms: $x^2 - 4xy + 4y^2 - 4x + 8y + 7 = 16 + 16y + 4y^2 - 16y - 8y^2 + 4y^2 - 16 - 8y + 8y + 7$

Step 5: Further simplify: $x^2 - 4xy + 4y^2 - 4x + 8y + 7 = 16 + 4y^2 - 8y^2 - 16 + 7$

Step 6: Combine like terms: $x^2 - 4xy + 4y^2 - 4x + 8y + 7 = -4y^2 + 7$

So, the expression $x^2 - 4xy + 4y^2 - 4x + 8y + 7$ when $x - 2y = 4$ is equal to $-4y^2 + 7$.