Giải thích các bước giải:

Bạn kiểm tra lại đề bài câu 3

$\begin{array}{l}
1){a^2} - 4ab + 5{b^2} - 4bc + 4{c^2}\\
 = \left( {{a^2} - 4ab + 4{b^2}} \right) + \left( {{b^2} - 4bc + 4{c^2}} \right)\\
 = {\left( {a - 2b} \right)^2} + {\left( {b - 2c} \right)^2}\\
2)5{x^2} + {y^2} + {z^2} + 4xy - 2xz\\
 = \left( {4{x^2} + 4xy + {y^2}} \right) + \left( {{x^2} - 2xz + {z^2}} \right)\\
 = {\left( {2x + y} \right)^2} + {\left( {x - z} \right)^2}\\
3)9{x^2} + 25 - 6xy + 2{y^2} - 10y\\
 = \left( {9{x^2} - 6xy + {y^2}} \right) + \left( {{y^2} - 10y + 25} \right)\\
 = {\left( {3x - y} \right)^2} + {\left( {y - 5} \right)^2}\\
4)13{x^2} + 4x - 12xy + 4{y^2} + 1\\
 = \left( {9{x^2} - 12xy + 4{y^2}} \right) + \left( {4{x^2} + 4x + 1} \right)\\
 = {\left( {3x - 2y} \right)^2} + {\left( {2x + 1} \right)^2}\\
5){x^2} + 4{y^2} + 4x - 4y + 5\\
 = \left( {{x^2} + 4x + 4} \right) + \left( {4{y^2} - 4y + 1} \right)\\
 = {\left( {x + 2} \right)^2} + {\left( {2y - 1} \right)^2}\\
6)4{x^2} - 12x + {y^2} - 4y + 13\\
 = \left( {4{x^2} - 12x + 9} \right) + \left( {{y^2} - 4y + 4} \right)\\
 = {\left( {2y - 3} \right)^2} + {\left( {y - 2} \right)^2}\\
7){x^2} + {y^2} + 2y - 6x + 10\\
 = \left( {{x^2} - 6x + 9} \right) + \left( {{y^2} + 2y + 1} \right)\\
 = {\left( {x - 3} \right)^2} + {\left( {y + 1} \right)^2}\\
8)4{x^2} + 9{y^2} - 4x + 6y + 2\\
 = \left( {4{x^2} - 4x + 1} \right) + \left( {9{y^2} + 6y + 1} \right)\\
 = {\left( {2x - 1} \right)^2} + {\left( {3y + 1} \right)^2}\\
9){y^2} + 2y + 5 - 12x + 9{x^2}\\
 = \left( {9{x^2} - 12x + 4} \right) + \left( {{y^2} + 2y + 1} \right)\\
 = {\left( {3x - 2} \right)^2} + {\left( {y + 1} \right)^2}\\
10){x^2} + 26 + 6y + 9{y^2} - 10x\\
 = \left( {{x^2} - 10x + 25} \right) + \left( {9{y^2} + 6y + 1} \right)\\
 = {\left( {x - 5} \right)^2} + {\left( {3y + 1} \right)^2}
\end{array}$

`1) =(a^2-4ab+4b^2)+(b^2-4bc+4c^2)`

`=(a-2b)^2+(b-2c)^2 `

`2) =(4x^2+4xy+y^2)+(x^2-2xz+z^2`

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

`3) =(9x^2-6xy+y^2)+(y^2-10y+25)`

`=(3x-2y)^2+(2x+1)^2`

`5)=(x^2+4x+4)+(4y^2-4y+1)`

`=(x+2)^2+(2x+1)^2`

`6) =(4x^2-12x+9)+(y^2-4y+4)`

`=(x-3)^2+(y+1)^2`

`8) =(4x^2-4x+1)+(9y^2+6y+1)`

`=(2x-1)^2+(3y+1)^2`

`9)=(9x^2-12x+4)+(y^2+2y+1)`

`=(3x-2)^2+(y+1)^2`

`10)=(x^2-10x+25)+(9y^2+6y+1)`

`=(x-5)^2+(3y+1)^2`