Toán Lớp 8: 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)

Question

Toán Lớp 8:  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)

myngocla · Answer

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

quynhthanhnhu · Answer

Giải đáp:       Lời giải và giải thích chi tiết:     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