Toán Lớp 8: Hép mi Rút gọn biểu thức: a, (x + y)²+ (x – y)² b, 2(x – y)(x + y) + (x + y)² + (x – y)² c, (x – y + z)² + (z – y)² + 2(x – y + z)(y –

Question

Toán Lớp 8:  Hép mi Rút gọn biểu thức: a, (x + y)²+ (x – y)² b, 2(x – y)(x + y) + (x + y)² + (x – y)² c, (x – y + z)² + (z – y)² + 2(x – y + z)(y – z)

maitrucloan · Answer

$  $   a,   (x+y)^2 + (x-y)^2   =x^2 +2xy + y^2 +x^2 - 2xy + y^2   = 2x^2 + 2y^2   $  $   b,   2 (x-y)(x+y) + (x+y)^2 + (x-y)^2   = (x-y)^2 + 2 (x-y)(x+y) + (x+y)^2   = (x-y +x+y)^2   = (2x)^2   =4x^2   $  $   c,   (x-y+z)^2 + (z-y)^2 + 2 (x-y+z)(y-z)   = (x-y+z)^2 + 2 (x-y+z)(y-z)+(y-z)^2   = (x-y+z + y-z)^2   = x^2

quynhthanhnghi · Answer

a, (x + y) 2  + (x &ndash; y) 2        = x 2  + 2xy + y 2  + x 2  &ndash; 2xy + y 2        = 2x 2  + 2y 2        b, 2(x &ndash; y)(x + y) + (x + y) 2  + (x &ndash; y) 2        = [(x + y) + (x &ndash; y)] 2         = (2x) 2  = 4x 2        c, (x &ndash; y + z) 2  + (z &ndash; y) 2  + 2(x &ndash; y + z)(y &ndash; z)       = (x &ndash; y + z) 2  + 2(x &ndash; y + z)(y &ndash; z) + (y &ndash; z) 2        = [(x &ndash; y + z) + (y &ndash; z)] 2         = x 2