giúp e với ạ !!!!!!!!

Đáp án + Giải thích các bước giải :

Bài `14` :

`1, x^2 - 2x + 1 - y^2 + 2x - 1`

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

`= x^2 - y^2`

`= ( x - y ) * ( x + y )` .

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`2, x^2 - 4x + 4 - y^2 - 6y - 9`

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

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

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

`= ( x - y - 5 ) * ( x + y + 1 )` .

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`3, 4x^2 - 4x + 1 - y^2 - 8y - 16`

`= [ (2x)^2 - 2 * 2x * 1 + 1^2 ] - ( y^2 - 2 * y * 4 - 4^2 )`

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

`= ( 2x - 1 - y + 4 ) * ( 2x - 1 + y - 4 )`

`= ( 2x - y + 3 ) * ( 2x + y - 5 )` .

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`4, x^2 - 2xy + y^2 - z^2 + 2zt - t^2`

`= ( x^2 - 2xy + y^2 ) - ( z^2 - 2zt + t^2 )`

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

`= ( x - y - z + t ) * ( x - y + z - t )` .

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`5, ( x + y )^2 - 2 * ( x + y ) + 1`

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

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

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`6, ( x^2 + x + 1 )^2 + 2x * ( x^2 + x + 1 ) + x^2`

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

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

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

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

`= [ ( x + 1 )^2 ]^2` .

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`@` Áp dụng :

`A^2 - B^2 = ( A - B ) * ( A + B )` .

`A^2 - 2AB + B^2 = ( A - B )^2` .

`A^2 + 2AB + B^2 = ( A + B )^2` .

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