A)(2+1)×(2^2+1)×(2^4+1)×(2^8+1) B)(x-y-z)^2 C)(2x+y+3)^2 D)(x-2y-3z)^2 Bài rút gọn lớp 8

0 bình luận về “A)(2+1)×(2^2+1)×(2^4+1)×(2^8+1) B)(x-y-z)^2 C)(2x+y+3)^2 D)(x-2y-3z)^2 Bài rút gọn lớp 8”

1. Giải thích các bước giải:

   `A)(2+1)×(2^2+1)×(2^4+1)×(2^8+1) ` 

   `=3*(2^2+1)*(2^4+1)*(2^8+1)`

   `=3*5*17*257`

   `=255*257`

   `=65535`

   `B)(x-y-z)^2`

   `=(x-y-z)(x-y-z)`

   `=x(x-y-z)-y(x-y-z)-z(x-y-z)`

   `=x^2+(-xy-xy)+(-xz-xz)+y^2+(yz+yz)+z^2`

   `=x^2-2xy-2xz+y^2+2yz+z^2`

   `C)(2x+y+3)^2`

   `=(2x+y+3)(2x+y+3)`

   `=2x(2x+y+3)+y(2x+y+3)+3(2x+y+3)`

   `=4x^2(+2xy+2xy)+(6x+6x)+y^2+(3y+3y)+9`

   `=4x^2+4xy+12x+y^2+6y+9`

   `D)(x-2y-3z)^2`

   `=(x-2y-3z)(x-2y-3z)`

   `=x^2-2xy-3xz-2yx+4y^2+6yz-3zx+6zy+9z^2`

   `=x^2-4xy-6xz+4y^2+12yz+9z^2`

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2. `1)(2+1).(2^2+1).(2^4+1).(2^8+1)`

   `=1.(2+1).(2^2+1).(2^4+1).(2^8+1)`

   `=(2-1).(2+1).(2^2+1).(2^4+1).(2^8+1)`

   `=(2^2-1).(2^2+1).(2^4+1).(2^8+1)`

   `=(2^4-1).(2^4+1).(2^8+1)`

   `=(2^8-1).(2^8+1)`

   `=2^16-1`

   `=65536-1`

   `=65535.`

   Ta có HĐT cho ba số: `(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca.`

   Ta áp dụng có:

   `2)(x-y-z)^2`

   `=[x+(-y)+(-z)]^2`

   `=x^2+(-y)^2+(-z)^2+2.x.(-y)+2.(-y).(-z)+2.(-z).x`

   `=x^2+y^2+z^2-2xy+2yz-2xz.`

   `3)(2x+y+3)^2`

   `=(2x)^2+y^2+3^2+2.2x.y+2.y.3+2.2x.3`

   `=4x^2+y^2+9+4xy+6y+12x.`

   `4)(x-2y-3z)^2`

   `=[x+(-2y)+(-3z)]^2`

   `=x^2+(-2y)^2+(-3z)^2+2.x.(-2y)+2.(-2y).(-3z)+2.(-3z).x`

   `=x^2+4y^2+9z^2-4xy+12yz-6xz.`

    

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