33) $(x+y)^{5}$ -$x^{5}$ -$y^{5}$

=$x^{5}$ + $5x^{4}$y +$10x^{3}$$y^{2}$+$10x^{2}$$y^{3}$+$5xy^{4}$+$y^{5}$-$x^{5}$-$y^{5}$ 

=$5x^{4}$y+$10x^{3}$$y^{2}$+$10x^{2}$$y^{3}$+$5xy^{4}$ 

=5xy($x^{3}$+$2x^{2}y$+$2xy^{2}$+$y^{3}$)

=5xy[($x^{3}$+$y^{3}$)+2xy(x+y)]

=5xy[(x+y)($x^{2}$-xy+$y^{2}$)+2xy(x+y)]

=5xy(x+y)($x^{2}$+xy+$y^{2}$)

34) $(x^{2}+y^{2})^{3}$`+`$(z^{2}-x^{2})^{3}$`-`$(y^{2}+z^{2})^{3}$

= $x^{6}$+$3x^{4}$$y^{2}$+$3x^{2}$$y^{4}$+$y^{6}$+$z^{6}$- $3x^{2}$$z^{4}$+ $3x^{4}$$z^{2}$ 

=-3[$x^{2}$($x^{2}$$y^{2}$-$x^{2}$$z^{2}$-$z^{2}$$y^{2}$+$z^{4}$)-$y^{2}$($x^{2}$$y^{2}$-$x^{2}$ $z^{2}$-$x^{2}$$y^{2}$+$z^{4}$)] 

=3($x^{2}$$y^{2}$)($x^{2}$$y^{2}$-$x^{2}$$z^{2}$-$z^{2}$$y^{2}$+$z^{4}$) 

Đáp án+Giải thích các bước giải:

 `33) (x + y)^{5} - x^{5} - y^{5}`

`= x^{5} + 5x^{4}y + 10x^{3}y² + 10x²y³ + 5xy^{4} + y^{5} - x^{5} - y^{5}`

`= 5x^{4}y+10x^{3}y^{2}+10x^{2}y^{3}+5xy^{4}`

`= 5xy(x³ + 2x²y + 2xy² + y³)`

`= 5xy . [ (x³ + y³) + 2xy(x + y)]`

`= 5xy . (x + y)(x² - xy  + y² + 2xy)`

`= 5xy(x + y)(x² + xy + y²)`

`34) (x² + y²)³ + (z² - x²)³ - (y² + z²)³`

`= x^{6} + 3x^{4}y² + 3x²y^{4} + y^{6} + z^{6} - 3z^{4}x² + 3z²x^{4} - x^{6} - y^{6} - 3y^{4}z^{2} - 3y²z^{4} - z^{6}`

`= 3x^{4}y² + 3x²y^{4} - 3z^{4}x² + 3z²x^{4} - 3y^{4}z^{2} - 3y²z^{4}`

`= 3(x^{4}y² + x²y^{4} - z^{4}x² + z²x^{4} - y^{4}z^{2} - y^{2}z^{4})`

`= 3 . [(x^{4}y² + x²y^{4}) - (z^{4}x² + y²z^{4}) + (z²x^{4} - y^{4}z²)]`

`= 3 . [x²y²(x² + y²) - z^{4}(x² + y²) + z²(x² + y²)(x² - y²)]`

`= 3(x² + y²)(x²y² - z^{4} + z²x² - z²y²)`

`= 3(x² + y²) . [(x²y² + z²x²) - (z^{4} + z²y²)]`

`= 3(x² + y²) . [x²(y² + z²) - z²(y² + z²)]`

`= 3(x² + y²)(y² + z²)(x² - z²)`