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

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