Are you sure the directions don't have "solve the equation as x=___ and y=___"
2xy=2*30*2=120
x2 + y2 = x2 - 2xy + y2 + 2xy = (x - y)2 + 2xy = 72 + 2*8 = 49 + 16 = 65 You could, instead, solve the two equations for x and y and substitute, but the above method is simpler.
2y + 2xy' + 4y + 4xy' = 0 6y + 6xy' = 0 y' = -y/x
4x2 - 4x + 2xy - 2y = 4x(x - 1) + 2y(x - 1) = (x - 1)(4x + 2y) = 2(x - 1)(2x + y)
2(x - 1)(2x + y)
2xy substitute 3 for y and 5 for x 2(5)(3) = 30
2xy=2*30*2=120
no if 1 plus 1 equals 2 then 2 plus 2 equals 4.
x2 + y2 = x2 - 2xy + y2 + 2xy = (x - y)2 + 2xy = 72 + 2*8 = 49 + 16 = 65 You could, instead, solve the two equations for x and y and substitute, but the above method is simpler.
if y = 2- x then x^2 + 2x(2 - x) = 3 ie x^2 + 4 x -2x^2 = 3 ie 4x - 3 = x^2 x^2 - 4x +3 = 0 = (x - 1)(x - 3) so x = 1 or 3 Check: y= 2 - 1 =1; x^2 = 1, 2xy = 2 x 1 x 1 = 2, 1 +2 = 3. y = 2 - 3 = -1; x^2 = 9, 2xy = 2 x 3 x -1 = -6, 9 + -6 = 3. QED.
2y + 2xy' + 4y + 4xy' = 0 6y + 6xy' = 0 y' = -y/x
4x2 - 4x + 2xy - 2y = 4x(x - 1) + 2y(x - 1) = (x - 1)(4x + 2y) = 2(x - 1)(2x + y)
(2xy-4x)+ (8y-16)=2xy-4x+8y-16, which factors as 2(x+4)(y-2)
2(x - 1)(2x + y)
( 2xy - 4x ) + ( 8y - 16)2 ( xy - 2x ) + 2 ( 4y - 8 ) Answer
1 plus 1 equals one fact
(x+y)2